Chapter 22 Problems. Problems Chapter 22 Page 1 of 3

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1 Chapte 22 Poblems Poblem 1: A +15 micoc chage is located 40 cm fom a +3.0 micoc chage. The magnitude of the electostatic foce on the lage chage and on the smalle chage (in N) is, espectively. Poblem 2: Two point paticles have chages q 1 and q 2 and ae sepaated by a distance d. Paticle q 2 expeiences an electostatic foce of 12 millin due to paticle q 1. If the chages of both paticles ae doubled and if the distance between them is doubled, what is the magnitude of the electostatic foce between them (in millin)? d +Q +Q x q Poblem 3: Two identical point chages +Q ae located on the y-axis at y=+d/2 and y=-d/2, as shown in the Figue. A thid chage q is placed on the x- axis. At what distance fom the oigin is the net foce on q a maximum? Poblem 4: Two 2.0 gam balls hang fom lightweight insulating theads 50 cm long fom a common suppot point as shown in the Figue. When equal chages Q ae place on each ball they ae epelled, each making an angle of 10 degees with the vetical. What is the magnitude of Q, in micoc? Q T θ Q Poblems Chapte 22 Page 1 of 3

2 Poblem 5: Fou point chages q, Q, -2Q, and Q fom a squae with sides of length as shown in the Figue. What is the magnitude of the esulting electostatic foce on the chage q due to the othe thee chages? -2Q Q q Q Q1 =1 m =1m θ θ Q2 x = 15 cm Poblem 6: Two 2.0 gam chaged balls hang fom lightweight insulating theads 1 m long fom a common suppot point as shown in the Figue. If one of the balls has a chage of 0.01 micoc and if the balls ae sepaated by a distance of 15 cm, what is the chage on the othe ball (in micoc)? Poblem 7: A chage +Q is fixed two diagonally opposite cones of a squae with sides of length. On anothe cone of the squae a chage of +5Q if fixed as shown in the Figue. On the empty cone a chage is placed, such that thee is no net electostatic foce acting on the +5Q chage. What chage is placed on the empty cone? +Q +5Q +Q q 4Q 2Q Q 2 θ Poblem 8: Thee point chages Q, 2Q, and 4Q fom a tiangle with sides of length and 2 as shown in the Figue. What angle does the esulting electostatic foce on the chage Q make with the positive x-axis (in degees)? F Poblems Chapte 22 Page 2 of 3

3 Poblem 9: Two identical point chages +Q ae located on the y-axis at y=+d/2 and y=-d/2 and a thid chage - 2Q is located at the oigin as shown in the Figue. The thee chaged +Q, +Q, and -2Q fom an electically neutal system called an electic quadupole. A chage q is placed on the x-axis a distance x = d fom the quadupole. At what is the net foce on q due to the quadupole? d +Q x -2Q +Q q Poblem 10: In the pevious poblem, what is the magnitude of foce on the chage q when x becomes vey lage compaed to the quadupole sepaation d. (Hint: take the limit of the quadupole foce on q when x << d.) Poblems Chapte 22 Page 3 of 3

4 Poblem 1: Chapte 23 Poblems What is the magnitude (in millin) and diection of the electostatic foce on a -2.0 micoc chage in a unifom electic field given by E = (100 N / C) xˆ? Poblem 2: Two point chages, +8 nanoc and -2 nanoc lie on the x-axis and ae sepaated by 6 metes as shown in the Figue. What +8 nc is the magnitude of the electic field (in N/C) at a point P on the x-axis a distance of 6 metes to the ight of the negative chage? 6 m -2 nc 6 m P Poblem 3: Two chages Q 1 and Q 2 ae sepaated by distance and lie on the x-axis with Q 1 at the oigin as shown in the figue. At a point P on the x-axis a distance /3 fom Q 1 the net electic field is zeo. What is the atio Q 1 /Q 2? Q1 /3 P Q2 Poblem 4: A paticle with a chage to mass atio of 0.1 C/kg stats fom est in a unifom electic field with magnitude, E = 10 N/C. How fa will the paticle move (in m) in 2 seconds? Poblem 5: A lage insulating sheet caies a unifom suface chage of density -1.2 micoc/m 2. A poton (with a mass of 1.67x10-27 kg) is eleased fom est at pependicula distance of 1.0 m fom the sheet. How much time (in micosec) elapses befoe the poton stikes the sheet? Poblems Chapte 23 Page 1 of 6

5 Poblem 6: At a distance of 1 mete fom an isolated point chage the electic field stength is 100 N/C. At what distance (in m) fom the chage is the electic field stength equal to 50 N/C? Poblem 7: The magnitude of the electic field 300 m fom a point chage Q is equal to 1,000 N/C. What is the chage Q (in C)? Poblem 8: A neon sign includes a long neon-filled glass tube with electodes at each end acoss which an electic field of 20,000 N/C. is placed. This lage field acceleates fee electons which collide with and ionize a potion of the neon atoms which emit ed light as they ecombine. Assuming that some of the neon ions (mass 3.35x10-26 kg) ae singly ionized (i.e. have chage e=1.6x10-19 C) and ae acceleated by the field, what is thei acceleation (m/s 2 )? a b c d e Poblem 9: Of the five chage configuations (a)-(e) shown in the Figue which one esults in the maximum magnitude of the electic field at the cente of the squae? Each configuation consists of a squae with eithe +Q, -Q, o no chage at each cone? Poblem 10: Two non-conducting infinite paallel ods ae a distance d apat as shown in the Figue. If the ods have equal and opposite unifom chage density, λ, what is the magnitude of the electic field along d +λ -λ Poblems Chapte 23 Page 2 of 6

6 a line that is midway between the two ods? Poblem 11: Two point chages, +8 nanoc and +2 nanoc ae sepaated by 6 metes. What is +8 nc the magnitude of the electic field (in N/C) midway between them? 6 m P 3 m +2 nc Poblem 12: Two point chages, Q and q, lie on the x-axis and ae sepaated by a distance of 1 mete as shown in the Figue. The chage Q lies at the oigin and the net electic field (on the x-axis) fom the two chages is zeo at the point x = 0.75 m. If the x-component of the electic field fom the two chages, E x = 13 N/C, at the point x =2 m (on the x-axis), what is Q (in nanoc)? Q 1 m E = 0 at x = 0.75 m 2 m q E = 13 N/C Poblem 13: Two point chages, +4 micoc and -1 micoc, lie on the x-axis and ae sepaated by a distance of 1 mete as shown in the Figue. If the +4 micoc lies at the oigin, at what point (o points) on the x-axis is the net electic field zeo? +4 µc 1 m x -1 µc Poblem 14: A -2 C point chage lies on the x-axis a distance of 1 mete fom an infinite nonconducting sheet of chage with a unifom suface chage density σ = 1 C/m 2 which lies in the yz-plane as shown in the Figue. At what point (o points) along the x-axis is the net electic field zeo? σ = 1 C/m 2 1 m -2 C x-axis Poblems Chapte 23 Page 3 of 6

7 λ P y=/2 λ Poblem 15: Two non-conducting semi-infinite ods lies along the x-axis as shown in the Figue. One od lies fom x = /2 to x = infinity and the othe od lies fom x = -/2 to and x = -infinity. The ods have chage unifomly distibuted along thei length with a linea density λ. What is the magnitude of the electic field at a point P located on the y-axis at y = /2? Poblem 16: A positive chage 8Q is distibuted unifomly along a thin cicula ing of adius. If the ing has a chage -Q located at its cente (see Figue), at what point, z, along the axis of the ing (othe than infinity) is the net electic field zeo? -Q Total Chage +8Q on ing z-axis Poblem 17: Two identical point chages +Q ae located on the y-axis at y=+d/2 and y=-d/2, as shown in the Figue. What is the magnitude of the electic field on the x-axis a distance x = d fom the oigin? d +Q x P Poblem 18: In the pevious poblem, what is the magnitude of the electic field on the x-axis when x becomes vey lage compaed to the sepaation d between the chages. (Hint: take the limit of the electic field when x >> d)? +Q Poblems Chapte 23 Page 4 of 6

8 P Chage on od = Q Semi-infinite od Poblem 19: A od caying a total chage Q unifomly distibuted along its length (constant λ) lies on the x-axis a distance fom a semi-infinite od with the same unifom chage density λ as the finite od as shown in the Figue. What is the magnitude of the net electic field at the point P on the x-axis a distance fom the end of finite od? +λ + + +λ λ -. Poblem 21: A non-conducting semi-infinite od lies along the x-axis as shown in the Figue (one end at x=0 and the othe at x=-infinity). The od has chage unifomly distibuted along its length with a linea density λ. What is the x-component of the electic Poblem 20: A thin plastic od is bent so that it makes a thee quates of a cicle with adius as shown in the Figue. If two quates of the cicle cay a unifom chage density +λ and one quate of the cicle caies a unifom chage density -λ, what is the magnitude of the electic field at the cente? field, E x, at a point P located a distance y above the end of the od? λ P y Poblem 22: An electic dipole is placed on the y-axis with +Q at y=0 and -Q at y=-d, as shown in the figue. What is the magnitude of the electic field at a point P located at x=d on the x-axis? d +Q -Q d P Poblems Chapte 23 Page 5 of 6

9 Poblem 23: As shown in the figue, a ball of mass M=2 kg and chage Q=3 C is suspended on a sting of negligible mass and length y-axis =1 m in a non-unifom electic field E( x) = axxˆ, x whee a=13.07 N/(Cm) is a constant. If the ball hangs at a non-zeo θ fom the vetical, what is θ? (Hint: gavity pulls the ball down with acceleation g=9.8 m/s 2.) θ x-axis +Q -Q Poblem 24: Two semicicula unifom nonconducting loops, each of adius, ae chaged oppositely to +Q and -Q, espectively. The loops ae now joined end to end to fom a cicula loop as shown in the figue. What is the magnitude of the electic field at the cente of the cicula loop? Q Poblem 25: Chage on od = Q A od caying a total chage Q unifomly distibuted along its length (constant λ) and a point chage Q both lie on the x-axis and ae sepaated by a distance as shown in the Figue. What is the magnitude of the net electic field at P on the x-axis a distance x = /3 fom the end of the od? Poblems Chapte 23 Page 6 of 6

10 Chapte 24 Poblems Poblem 1: Conside a spheical conducting shell S 1 of adius on which chage +Q is placed. Without touching o distubing it, this shell is now suounded concentically by a simila shell S 2 of adius 2 on which chage -Q is placed (see Figue). What is the magnitude of the electic field in the egion between the two shells ( < < 2)? Shell S 2 has chage -Q 2 Shell S 1 has chage +Q d t Poblem 2: In the pevious poblem, what is the electic field inside shell S 1 ( < )? Poblem 3: A solid insulating sphee of adius has chage distibuted unifomly thoughout its volume. What faction of the sphee s total chage is located within the egion < /2? Poblem 4: A solid insulating sphee of adius has a non-unifom volume chage distibution given by ρ() = a, whee a is a constant. What is the total chage Q of the insulating sphee? Poblem 5: In a cetain egion of space within a distibution of chage the electic field is given by E( ) = aˆ. It points adially away fom the oigin and has a magnitude E() = a, whee a = 150N/(Cm). How much electic chage (in nanoc) is located inside a shell with an inne adius of 0.5 metes and an oute adius of 1.0 metes? Poblems Chapte 24 Page 1 of 4

11 Poblem 6: In a cetain egion of space the electic field is given by E( ) = ( a / ) ˆ. It points adially away fom the oigin and has a magnitude E() = a/, whee a = 90Nm/C. How much electic chage (in nanoc) is located inside a sphee with adius = 0.5 metes? Poblem 7: In a cetain egion of space within a distibution of chage the electic field is given by E( x) = axxˆ. It points in the x diection and has a magnitude E x (x) = ax, whee a = 150N/(Cm). How much electic chage (in nanoc) is located inside the cube with sides of length = 2 m shown in the Figue? z-axis O y-axis x-axis Poblem 8: Conside a cube of sides =2 m, as shown in the figue. Suppose that a non-unifom electic field is pesent and is given by E( x) = ( a + bx) xˆ, whee a=1 N/C and b=0.5 N/(Cm). What is the total net chage within the cube (in picoc)? O y-axis x-axis 3 Insulato chage +Q Conducto 2 Net chage zeo on conducto Poblem 9: A solid insulating sphee of adius has a chage +Q distibuted unifomly thoughout its volume (the volume chage density ρ is constant). The insulating sphee is suounded by a solid spheical conducting shell with inne adius 2 and oute adius 3 as shown in the Figue. The conducto is in static equilibium and has a zeo net chage. What is the magnitude of the electic field at the point = 5/2 inside the conducto? z-axis Poblems Chapte 24 Page 2 of 4

12 Poblem 10: In the pevious poblem, what is the magnitude of the electic field at the point = 4 outside the conducto? Poblem 11: A thundestom foms a mysteious spheical cloud with a adius of 20 m. Measuements indicate that thee is a unifom electic field at the suface of the cloud that has a magnitude of 1,000 N/C and is diected adially inwad towad the cente of the cloud. What is the total net chage within the cloud (in micoc)? Poblem 12: A 6.0 micoc chage is at the cente of a cube 10 cm on a side. What is the electic flux (in Nm 2 /C) though one face of the cube? (Hint: think symmety and don t do an integal.) Poblem 13: A solid insulating sphee of adius has chage distibuted unifomly thoughout its volume (the volume chage density ρ is constant). The insulating sphee is suounded by a solid spheical conducto with inne adius and oute adius 2 as shown in the figue. The net chage on the conducto is zeo. What is the magnitude of the electic field at the point =3 outside the conducto? 2 Insulato ρ = chage/unit volume Conducto Zeo net chage Poblem 14: In the pevious poblem, what is the magnitude of the electic field at the point =3/2 inside the conducto? Poblem 15: In the pevious poblem, what is the magnitude of the electic field at the point =/2 inside the insulato? Poblems Chapte 24 Page 3 of 4

13 Poblem 16: A solid insulating sphee of adius has a chage +Q distibuted unifomly thoughout its volume (the volume chage density ρ is constant). The insulating sphee is suounded by a solid spheical conducto with inne adius and oute adius 2 as shown in the Figue. The conducto is in static equilibium and has a net chage +Q. What is the magnitude of the electic field at the point = /2 inside the insulating sphee? 2 Insulato ρ = chage/unit volume Conducto Zeo net chage Poblem 17: In the pevious poblem, what is the magnitude of the electic field at the point = 3/2 inside the conducto? Poblem 18: A point chage +Q is located at the cente of a solid spheical conducting shell with inne adius of and oute adius of 2 as shown in the Figue. In addition, the conducting shell has a total net chage of +Q. How much chage is located on the oute suface ( = 2) of the conducting shell? 2 +Q Net chage +Q on conducto Poblem 19: In the pevious poblem, what is the magnitude of the electic field in the egion < inside the hole in the conducting shell? Poblems Chapte 24 Page 4 of 4

14 Chapte 25 Poblems Poblem 1: If the potential diffeence between points A and B is equal to V A -V B = 3x10 4 Volts, how much wok (in millijoules) must be done (against the electic foce) to move a change paticle (Q = 3 micoc) fom point A to point B without changing the kinetic enegy of the paticle? Poblem 2: Eight identical point chages, Q, ae located at the cones of a cube with sides of length. What is the electic potential at the cente of the cube? (Take V = 0 at infinity as the efeence point.) Poblem 3: What is the electic potential enegy of the configuation of eight identical point chages, Q, at the cones of the cube with sides of length in the pevious poblem? Poblem 4: Two point chages Q 1 = Q and Q 2 = Q ae on the x-axis at x = + and x = - and a thid point chage Q 3 = Q is on the y-axis at the point y = as shown in the Figue. What is the electic potential diffeence, V = V 2 -V 1 between the point P 2 at the midpoint of the line between Q 1 and Q 3 and the point P 1 at the oigin? Q1=Q x = - y-axis Q3=Q y = 2 1 Q2=Q x = x-axis Poblem 5: Two point chages Q 1 = Q and Q 2 = Q ae on the x-axis at x = + and x = - and a thid point chage Q 3 = Q is on the y-axis at the point y = as shown in the pevious Figue. What is the electic potential enegy of this chage configuation? Poblems Chapte 25 Page 1 of 6

15 Q1=Q x = - y-axis Q3=Q Q2=Q x = x-axis Poblem 6: In the poblem 4, how much wok must be done (against the electic foce) to move the chage Q 3 fom the point y = on the y-axis to the oigin esulting in the configuation shown in the Figue? Poblem 7: Thee identical point chages, Q, ae located at the cones of a ight tiangle with sides of length as shown in the Figue. What is the electic potential at the point P that bisects the hypotenuse? (Take V = 0 at infinity as the efeence point.) Q P Poblem 8: What is the electic potential enegy of the configuation of thee identical point chages, Q, located at the cones of a ight tiangle with sides of length in the pevious poblem? Q Q Poblem 9: In poblem 7, how much wok is equied to move the chage located at the 90 o angle of the equilateal tiangle to the point P that bisects the hypotenuse? Q Q Q Poblems Chapte 25 Page 2 of 6

16 Poblem 10: Thee identical chaged paticles (Q = 3.0 micoc) ae placed at the vetices of an equilateal tiangle with side of length = 1 m and eleased simultaneously fom est as shown in the Figue. What is the kinetic enegy (in millij) of one of the paticles afte the tiangle has expanded to fou times its initial aea? Q Q Q Poblem 11: A unifom electic field E=10 V/m points in the x diection as shown in the Figue. Point A has coodinates (0,1m) and point B has coodinated (2m,2m), whee points ae labeled accoding to P=(x,y). What is the potential diffeence V B -V A (in Volts)? A 2m B E 40 o A 5 cm B E Poblem 12: A unifom electic field E=400 V/m cosses the x-axis at a 40 o angle as shown in the Figue. Point B lies on the x-axis 5 cm to the ight of the oigin A. What is the potential diffeence V B -V A (in Volts)? Poblem 13: A non-unifom electic field is given by 2 E ( x) = ax xˆ, whee a = 10 V/m 3 as shown in the Figue. Point B lies at x=y=3 m and point A is at the oigin (x=y=0). What is the potential diffeence V B -V A (in Volts)? A 3m B E(x) Poblems Chapte 25 Page 3 of 6

17 Poblem 14: The potential along the x-axis is given by V(x) = ax-bx 2, whee a=2 V/m and b=1 V/m 2. At what value(s) of x (in m) is the electic field equal to zeo? Poblem 15: The potential is given by V(x,y) = a/(x 2 +y 2 ), whee a = 2 Vm 2. What is the magnitude of the electic field (V/m) at the point, P = (x,y) = (1m,1m)? Poblem 16: The potential is given by V(x,y,z) = ax+by+cz 2, whee a = 3 V/m, b = -4 V/m,and c = 5 V/m 2. What is the magnitude of the electic field (in V/m) at the oigin, P=(x,y,z)=(0,0,0)? Poblem 17: Two thin concentic cicula plastic ods of adius and 2 have equal and opposite unifom chage densities -λ and +λ, espectively, distibuted along thei cicumfeences as shown in the Figue. What is the electic potential at the cente of the two cicles? (Take V = 0 at infinity as the efeence point.) +λ -λ 2 Poblem 18: A positive chage Q is distibuted unifomly along a thin cicula ing of adius. A negatively chaged paticle (chage -Q) is at the cente of the ing as shown in the Figue. What is the electic potential at a point on the z-axis of the ing a distance fom the cente. (Take V=0 at infinity as the efeence point.) -Q Total Chage +Q on ing z-axis Poblems Chapte 25 Page 4 of 6

18 Poblem 19: An infinitely long thin od lies along the y-axis and has a unifom linea chage density λ = 3 micoc/m as shown in the Figue. If point P 1 = (a,0) and point P 2 = (2a,b), whee P = (x,y), what is the potential diffeence V = V 2 -V 1 (in kilovolts)? λ = 3µC/m y-axis a 2a 1 2 b x-axis Chage Q on od Poblem 20: A positive chage Q is distibuted unifomly along a thin od of length as shown in the Figue. What is the electic potential at a point P on the axis of the od a distance fom the end of the od? (Take V = 0 at infinity as the efeence point.) P Poblem 21: A cicula plastic od of adius has a positive chage +Q unifomly distibuted along one-quate of its cicumfeence and a negative chage of -3Q unifomly distibuted along the est of the cicumfeence as shown in the Figue. What is the electic potential at the cente of the cicle? (Take V = 0 at infinity as the efeence point.)? -3Q +Q Poblem 22: The electic field at the suface of a solid spheical conducto (adius = 20 cm) points adially outwad and has a magnitude of 10 V/m. Calculate the electic potential (in Volts) at the cente of the conducting sphee. (Take V = 0 at infinity as the efeence point.) Poblems Chapte 25 Page 5 of 6

19 Poblem 23: A solid insulating sphee of adius has chage a total chage Q distibuted unifomly thoughout its volume (the volume chage density ρ is constant). If the electic potential is zeo at infinity and 12 Volts at the cente of the sphee, what is the potential at the suface = (in Volts)? Poblems Chapte 25 Page 6 of 6

20 Chapte 26 Poblems Poblem 1: What is the capacitance C of a solid spheical conducting shell with inne adius and oute adius 2? Poblem 2: An enegy of 9.0x10-3 Joules is stoed by a capacito that has a potential diffeence of 85 Volts acoss it. Detemine the capacitance of the capacito (in micof). Poblem 3: Capacito #1 with capacitance C and initial chage Q is connected in paallel acoss an initially unchaged capacito with capacitance 2C (#2). Afte the system comes to equilibium, what is the chage on capacito #1? Poblem 4: A chaged conducting sphee with a adius of 5 cm has a potential of 8 kilovolts elative to infinity. What is the electic field enegy density (in J/m 3 ) at a point nea the suface outside the conducto? Poblem 5: The electic field enegy density nea the suface of an isolated chaged conducting sphee with a adius of 5 cm is 0.1 J/m 3. What is the electic potential (in kilovolts) at the cente of the conducto? Poblems Chapte 26 Page 1 of 2

21 Poblem 6: In a cetain egion of space the electic field is given by, E = Ayx$, whee A=100 V/m 2. The electic field points in the x diection and has a constant magnitude given by E(y)=Ay. What is the total amount of electic potential enegy (in millijoules) contained in the electic field within the cube with sides of length =20 metes shown in Figue? x-axis O z-axis y-axis Poblem 7: Given an open-ai paallel-plate capacito of plate aea A and plate sepaation d as shown in the Figue. A flat slice of conducting mateial (thickness b; b<d) of the same aea A is now caefully inseted between the plates paallel to them without touching. If the chage Q on the capacito was unchanged duing this opeation, must the metal slice be foced between the plates o will it be pulled in by electostatic foces, and what is the new capacitance? d +Q -Q b Poblems Chapte 26 Page 2 of 2

22 Chapte 27 Poblems Poblem 1: Wie B is thee times longe than wie A, and the two wies have the same volume. If both wies ae made of the same substance and if the esistance of wie A is 9 Ohms, what is the esistance of wie B (in Ohms). 1 Ω Poblem 2: How much cuent passes though the 1 Ω esisto in the cicuit shown in the Figue? I 2 Ω 3 Ω Poblem 3: Conside a long staight cylindical wie with adius caying the nonunifom cuent density, J()=a 2, whee is the distance fom the cente axis of the wie. How much total cuent I passes though the wie? Poblem 4: Conside a long staight cylindical wie with adius = 0.1 m is caying the non-unifom cuent density which points along the axis of the wie and has a magnitude, J() = a/, whee is the distance fom the cente axis of the wie. If a = 2 A/m, how much total cuent I passes though the wie (in A)? Poblems Chapte 27 Page 1 of 2

23 A B Poblem 5: Conside the infinite chain of esistos shown in the Figue. Calculate the effective esistance,, (in Ohms) of the netwok between the teminals A and B given that each of the esistos has esistance = 1 Ohm. Poblems Chapte 27 Page 2 of 2

24 Chapte 28 Poblems Poblem 1: Conside the cicuit consisting of an EMF and thee esistos shown in the Figue. How much cuent flows though the 4 Ω esisto (in Amps)? 0 = 3 Ω 1 = 4 Ω 24 V 2 = 12 Ω Poblem 2: A constant powe P is supplied to a tansmission line of esistance by a powe station. If the powe dissipated in the tansmission line is 200 Watts when the powe station delives an EMF of 10 Volts, how much powe is dissipated in the tansmission line (in W) when the powe station delives an EMF of 20 Volts (assuming the same powe is supplied in both cases)? Poblem 3: A capacito C with an initial chage Q dischages though a esisto. How many time constants τ = C must elapse in ode fo the capacito to lose 2/3 of its chage? Poblem 4: The capacito in the Figue is initially unchaged. Afte the switch is closed (EMF = 12 V), what is the magnitude of the potential diffeence acoss the capacito (in V) when the chage on the capacito eaches one-thid of its maximum value? 12V C Poblem 5: A chaged capacito C has a esistance connected acoss its teminals to fom the C cicuit shown in the Figue. If it takes 2 seconds fo the capacito to loose one-half of its stoed enegy, how long does it take (in s) fo it to loose 90% of its initial chage? C Poblems Chapte 28 Page 1 of 2

25 Poblem 6: A capacito, C, is (fully) chaged by connecting it to a 10 Volt EMF and then is allowed to dischage though a 2 Ω esisto as shown in the Figue? What is the cuent, I, in the cicuit (in A) when the stoed enegy in the capacito has dopped to 50% of its initial value? C I = 2 Ω Poblem 7: A "leaky" capacito's faulty insulation allows chage to pass slowly fom one plate to the othe. Suppose that a chaged leaky 2.0 micof capacito's potential diffeence dops to one-fouth its initial value in 2.0 sec. What is the equivalent esistance between the capacito plates, in megaohms? (Hint: the leaky capacito foms an C cicuit.) C C left Poblem 8: Conside the dischaging of the two capacitos shown in the Figue. Both capacitos have equal capacitance C and both have an initial chage of 8 micoc. When the switches ae closed the capacito an the left will dischage though a single esisto with esistance, while the capacito on the ight dischages though two equal esistos with esistance connected in paallel. If the switches ae closed simultaneously, how much chage is on the ight capacito (in micoc) when the left capacito s chage is 4 micoc? ight Poblems Chapte 28 Page 2 of 2

26 Poblem 1: Chapte 29 Poblems A chaged paticle, Q = 0.5 C, entes a egion with a unifom magnetic field B = 2 xˆ + 3yˆ + 4zˆ (in Tesla). If its velocity is given by v = 2 xˆ + 3yˆ + 2zˆ (in m/s), what is the magnitude of the magnetic foce on the paticle (in N)? Poblem 2: A chaged paticle, Q=0.5 C, and mass M = 200 gams entes a egion with a unifom magnetic field B = 2xˆ 1yˆ (in Tesla). What is the magnitude of the magnetic foce on the paticle (in N), if its velocity is v = 4xˆ 2 yˆ (in m/s)? Poblem 3: One end of a staight wie segment is located at (x,y,z) = (0,0,0) and the othe end is at (1m,2m,3m). A cuent of 2 Amps flows though the segment. The segment sits in a unifom magnetic field B = 2xˆ 1yˆ (in Tesla). What is the magnitude of the magnetic foce (in N) on the wie segment? Poblem 4: An electic powe tansmission line located an aveage distance of 20 m above the eath's suface caies a cuent of 800 Amps fom east to west, in a egion whee the eath's magnetic field is 0.8 gauss due noth at 60 o below the hoizontal. What is the magnitude of the foce pe mete on the line (in millin/m)? Poblem 5: A chaged paticle, Q=0.1 C, taveling in the x-diection with velocity v = v xˆ 0 entes a egion of space that has an electic field in the y-diection given by E = E yˆ 0 with E 0 = 10 Volts and a magnetic field in the z- diection given by B = B zˆ with B 0 = 0.2 Tesla. If the paticle expeiences 0 Poblems Chapte 29 Page 1 of 3

27 no net foce and continues with the same speed and diection, what is its speed v 0 (in m/s)? Poblem 6: A chaged paticle taveling in the y-diection with a momentum of 0.01 kg m/s entes a egion of space that has a unifom 1 Tesla magnetic field in the z-diection as shown the Figue. If the paticle entes the magnetic field at the point A and then exits the magnetic field at the point B 0.5 m located a distance of 0.5 m to the left of the point A, what is the chage of the paticle (in millic)? B-out Poblem 7: A chaged paticle taveling in the y-diection entes a egion of space that has a unifom 2 Tesla magnetic field in the z-diection as shown in the Figue. If the paticle has a chage of 0.1 C and a mass of 0.2 kg how long (in seconds) does it take fo the paticle to evese diection and exit the egion? v B-out Poblem 8: Paticle #1 and paticle #2 tavel along the y-axis and ente a egion of space that has a unifom 2 Tesla magnetic field in the z- diection as shown in the Figue. Both paticles have the same chage, Q=0.1 C, and both have the same speed, v = 10 m/s. If the paticles ae a distance x = x 2 -x 1 = 0.3 metes apat when they exit the egion, what is the diffeence in thei mass, M = M 2 -M 1 (in gams)? v y-axis 1 2 x B-out x-axis Poblems Chapte 29 Page 2 of 3

28 Poblem 9: A cicula loop of wie of adius = 1 m is caying a cuent of 2 Amps as shown in the Figue, A paticle with chage Q = 3x10-3 C is on the axis of the loop (z-axis) a distance of d = 0.5 metes away fom the loop and is moving with a speed of 2x10 6 m/s along the x-axis (i.e. pependicula to the axis of the loop). What is the magnitude of the magnetic foce (in millin) on the paticle due to the loop? z-axis d I v Poblems Chapte 29 Page 3 of 3

29 Chapte 30 Poblems Poblem 1: The bent wie caies cuent I, as shown the Figue. What is the magnetic field at point P, at distance d diectly opposite the 90 o bend (k = µ 0 /4π)? A I B d P Poblem 2: Two semi-infinite staight pieces of wie ae connected by a cicula loop segment of adius as shown in the Figue. If extapolated to thei intesection point staight wies would fom a 30 o angle. If the wies cay a cuent I, what is the magnitude of the magnetic field at the cente of the cicula ac (k = µ 0 /4π)? I 30 o Poblem 3: Thee concentic cuent loops have adii, 2, and 3, as shown in the Figue. The loop with adius 2 caies a cuent of 2I and the loop with adius 3 caies a cuent of 3I in the same diection (counte-clockwise). If the net magnetic field at the cente of the thee loops is zeo, what is the magnitude and diection of the cuent in the loop with adius? 3 2 2I 3I Poblems Chapte 30 Page 1 of 6

30 Poblem 4: Two semi-infinite staight pieces of wie ae connected by a cicula loop segment of adius as shown in the Figue. If the two staight pieces of wie ae pependicula to each othe and if the cicuit caies a cuent I, what is the magnitude of the magnetic field at the cente of the cicula ac (k = µ 0 /4π)? I I Poblem 5: An infinitely long staight wie caies a cuent I 1, and a wie loop of adius caies a cuent I 2 as shown in the Figue. If I 1 = 4I 2, and if the net magnetic field at the cente of the cicula loop is zeo, how fa is the cente of the loop fom the staight wie? I 2 y I 1 Poblem 6: Fou infinitely long paallel wies each caying a cuent I fom the cones of squae with sides of length as shown in the Figue. If thee of the wie cay the cuent I in the same diection (out of the page) and one of the wies caies the cuent I in the opposite diection (into the page), what is the net magnetic field at the cente of the squae (k = µ 0 /4π)? I-out I-out I-in I-out Poblems Chapte 30 Page 2 of 6

31 Poblem 7: Two infinitely long paallel wies ae a distance d apat and cay equal paallel cuents I in the same diection as shown the Figue. If the wies ae located on the y-axis at y = d/2 and y = -d/2, what is the distance x to the point P on the positive x-axis whee the magnitude of the magnetic field is maximum? I-out d y-axis x P x-axis I-out Poblem 8: Two infinitely long paallel wies ae a distance d apat and cay equal antipaallel cuents I as shown in the Figue. If the wies ae located on the y-axis at y=+d/2 and y=-d/2, what is the magnitude of the magnetic field at a point x on the x-axis (assume that x >> d and let k = µ 0 /4π)? y-axis I-out d x P x-axis I-in Poblem 9: Two infinitely long paallel wies ae a distance d apat and cay equal antipaallel cuents I as shown in the Figue. If the wies ae located on the y-axis at y = 0 and y = d, what is the magnitude of the magnetic field at the point x = d on the x-axis? I-out d I-in y-axis x = d P x-axis Poblems Chapte 30 Page 3 of 6

32 Poblem 10: A single infinitely long staight piece of wie caying a cuent I is split and bent so that it includes two half cicula loops of adius, as shown in the Figue. If cuent I 1 goes though the top loop and cuent I 2 though the lowe loop (with I = I 1 +I 2 ) and if I 2 = 2I 1 what is the magnitude of the magnetic field at the cente of the cicle (k = µ 0 /4π)? Poblem 11: A single infinitely long staight piece of wie caying a cuent I is split and bent so that it includes two half cicula loops of adius, as shown in the Figue. If cuent I 1 goes though the top loop (and I-I 1 though the lowe loop) and if the magnetic field at the cente of the loops is B = π ki /( 2)$ z whee the z-axis is out of the pape, what is the cuent I 1? I I I 1 I 1 I 2 I-I 1 Poblem 12: Thee coaxial cuent loops of adius each cay a cuent I as shown in the Figue. The cente loop caies the cuent in the opposite diection fom the oute two loops. If the centes of the cuent loops ae a distance apat what is the magnitude of the magnetic field at the cente of the middle cuent loop (k = µ 0 /4π)? I 1 I 2 I 3 z-axis Poblems Chapte 30 Page 4 of 6

33 Poblem 13: Thee infinitely long paallel staight wies lie in the xy-plane as shown in the Figue. The middle wie caes a cuent I to the left while the top and bottom wies each cay a cuent I to the ight. If the wies ae a distance d apat, what is the magnitude of the magnetic field at the midpoint P between the top and middle wie (k = µ 0 /4π)? Poblem 14: In the pevious poblem, what is the y-component of the foce pe unit length exeted on the top wie due to the othe two wies (k = µ 0 /4π)? d d I I I P y x Poblem 15: The Figue shows the coss section of a solid cylindical conducto with adius. The conducto is caying a unifomly distibuted cuent I (out of page). Find the magnitude of the magnetic field, B, inside the conducto a distance = /4 fom the cente (k = µ 0 /4π). I-out Poblem 16: The Figue shows the coss section of a solid cylindical conducto with adius 0.2 m. The conducto is caying a unifomly distibuted cuent I (out of page). If the magnitude of the magnetic field inside the conducto a distance 0.1 m fom the cente is 0.1 micotesla, what is the total cuent, I, caied by the cylindical conducto (in Amps)? Itot = 0.2m Poblems Chapte 30 Page 5 of 6

34 Poblem 17: An infinite conducting sheet of thickness T lies in the xz-plane and caies a unifomly T distibuted cuent density J in the z diection as shown in the Figue. What is the magnitude z and diection of the magnetic field at distance d above the sheet (in the +y diection, k = µ 0 /4π)? y J x Poblem 18: A long staight cylindical wie with adius (see the Figue) is caying a non-unifom cuent density which points along the axis of the wie and has a magnitude, J() = a/, whee a is a constant and is the distance fom the cente axis of the wie. What is the magnitude of the magnetic field inside the wie a distance fom the cente (0 < < )? J-out Poblem 19: The Figue shows the coss section of a solid cylindical conducto with adius 3 with a cylindical hole of adius. The conducto is caying a unifomly distibuted cuent I (out of page). Find the magnitude of the magnetic field, B, at a distance = 2 fom the cente. I-out 3 Poblems Chapte 30 Page 6 of 6

35 Chapte 31 Poblems Poblem 1: A long staight wie caies cuent I. Neaby and lying in the same plane is a cicula loop, as shown in the Figue. If the loop is moved towad the wie, what will be the diection of the cuent induced in the loop (if any) and what will be the diection of any electomagnetic foce exeted on the loop? I Poblem 2: A magnetic field given by B(t) = at+b with a = 1 T/s and b = -1 T is diected pependicula to the plane of a cicula coil of 10 tuns and adius 0.2 m. If the coil's total esistance is 1.58 Ohms, how much powe (in Watts) is dissipated at time t = 1 s? Poblem 3: A 25-tun coil of esistance 3 Ohms has aea of 8 cm 2. Its plane is pependicula to a magnetic field given by B(t) = 0.4t - 0.3t 2 (whee B is in Tesla and t is in seconds). What is the induced cuent in the coil (in millia) at t = 1 second? Poblem 4: A unifom time dependent magnetic field given by B(t) = at 2 with a = 0.3 T/s 2 is diected pependicula to the plane of a squae wie loop with sides of length 0.5 m. If the total esistance of the squae wie is 0.4 Ohms, how much total enegy (in Joules) is dissipated by heat in the wie duing the time fom t = 0 to t = 10 seconds? Poblems Chapte 31 Page 1 of 6

36 Poblem 5: A single wie squae loop with aea A = 100 cm 2 otates with a constant angula velocity in the magnetic field of the eath (about 100 micot). The axis of otation goes though one side of the squae loop (in the plane of the loop) and is pependicula to the magnetic field as shown in the Figue. If the peiod of the otation is one second, what is the maximum EMF geneated in the loop (micov)? B Squae oop Axis Poblem 6: How will the answe in the pevious poblem change if one moves the axis of otation of the loop fom the side to the cente of the loop (in the plane of the loop) as shown in the Figue? B Squae oop Axis Poblem 7: A moveable (massless and fictionless) ba is being moved at a constant velocity of 3 m/s fom left to ight along two conducting ails as shown in the Figue. The two conducting ails make an angle of 45 o with each othe and togethe with the moving ba fom a ight tiangle. If the system is immesed in a unifom magnetic field (out of the pape) with magnitude B = 0.5 Tesla and if the ba was at x = 0 at t = 0, what is the magnitude of the induced EMF in the ight tiangle (in Volts) at t = 2 seconds? 45 o x v B-out Poblems Chapte 31 Page 2 of 6

37 Poblem 8: A wie cicula loop with a esistance pe unit length of 0.5 Ohms/mete is placed in = vt a unifom magnetic field given by B = B0 zˆ, with B 0 = 2 Tesla, as shown in the Figue (z is out of the pape). If the adius of the cicula loop is inceasing at a constant ate given by (t) = vt with v = 0.5 m/s, what is the magnitude of the induced EMF (in Volts) at t = 10 seconds? B-out Poblem 9: In the pesious poblem, what is the magnitude (in Amps) and diection of the induced cuent in the loop at t = 10 seconds? Poblem 10: A moveable (massless and fictionless) ba with a length of = 1 mete is being moved at a constant velocity of 10 m/s fom left to ight along two conducting ails by an extenal foce, F, as shown in the Figue. If the system is immesed in a unifom magnetic field (out of the pape) with magnitude B=2 T, what is the induced cuent (in Amps) in the 5 Ohm esisto? = 5Ω x v B-out Poblems Chapte 31 Page 3 of 6

38 Poblem 11: A moveable (massless and fictionless) conducting od is pulled by an extenal foce so that it otates with a constant angula velocity along a semicicula loop of wie with adius of = 0.5 m as shown in the Figue. The otating od is connected at the cente of the semicicula loop to a stationay od that is also in contact with the semicicula loop. If the entie system is placed in a unifom 2 Tesla magnetic field (out of the page), and if it takes 1 second fo the angle between the two ods to go fom θ = 0 to θ = 90 o, what is the magnitude of the induced emf (in Volts) in the cicuit? I A Poblem 12: A cuent I flows though a esisto with =25 kω, a capacito with C=4 millif, and an inducto with =7 Heny as shown in the Figue. At a time when Q=8 millic and the cuent I=0.2 milliamps and is changing at a ate di/dt=1.0 A/s, what is the potential diffeence V B -V A (involts)? C + - Q B-out = 0.5 m B θ F 1 A I Poblem 13: A cuent I flows though a esisto with = 333 Ω, and two inductos in paallel with 1 = 2 Heny and 2 = 4 Heny as shown in the Figue. At a 2 B Poblems Chapte 31 Page 4 of 6

39 time when the cuent I = 1.0 milliamps and is changing at a ate di/dt = -1.0 A/s, what is the potential diffeence V B -V A (in Volts)? Poblem 14: What is the magnitude of the unifom magnetic field (in Tesla) that contains as much enegy pe unit volume as a unifom 3,000 V/m electic field? 1 A I C + - Q B Poblem 15: A cuent I flows though a esisto with = 2 Ω, a capacito with C = 3 millif, and and two inductos in paallel ( 1 = 1 milliheny and 2 = 3 milliheny) as shown in the Figue. At a time when Q = 0.6 micoc and the cuent I = 0.2 milliamps and is deceasing at a ate of 0.8 Amps/s, what is the potential diffeence V B -V A (millivolts)? 2 Poblem 16: In an cicuit whee = 120 millih and = 15 ohms, if the switch is closed at t = 0 how long (in milli-seconds) does it take fo the cuent to each 75% of its final value? Poblem 17: In an cicuit whee = 120 millih and = 15 ohms, if the switch is closed at t = 0 how long (in milli-seconds) does it take fo the stoed enegy in the inducto to each 50% of its maximum value? Poblems Chapte 31 Page 5 of 6

40 Poblem 18: Conside the cicuit shown in the Figue which consists of two equal inductos,, and two equal esistos,, and an EMF. If = 4 milliheny and = 2 milliohms and if the switch is closed at t = 0, how long (in seconds) does it take EMF fo the total cuent in the cicuit to each 90% of its final value? I I1 I2 Poblem 19: Conside the cicuit shown in the Figue which consists a 8 Volt EMF, an inducto, = 4 H, and two esistos. If the switch is closed at t = 0, when (in seconds) is the cuent though the 2 Ω esisto equal to 1 Amp? 8V I 1 = 2Ω 2 = 4Ω I1 I2 = 4H Poblems Chapte 31 Page 6 of 6

41 Chapte 32 Poblems Poblem 1: A paallel-plate capacito whose plates have adius is being chaged by a cuent I. What is the magnitude of the magnetic field (in Tesla) between the plates a distance = /2 fom the cente? Poblem 2: A paallel-plate capacito whose plates have adius is ε being chaged though a esisto by an EMF ε as shown in the Figue. If the switch is closed at t = 0, what is the maximum magnitude of the magnetic field between the plates of the capacito a distance /2 fom the cente? (Note: k = µ 0 /4π) C Poblem 3: The potential diffeence, V C, acoss a 3 Faad paallel-plate capacito whose plates have adius = 2 cm vaies with time and is given by V C (t) = at, with a = 10 V/s. What is the magnitude of the magnetic field (in micot) between the plates of the capacito a distance fom the cente? Poblem 4: A 2 millifaad paallel-plate capacito whose plates ae cicula with adius = 0.5 cm is connected to an EMF-souce that inceases unifomly with time at a ate of 150 V/s. What is the magnitude of the magnetic field (in micotesla) between the plates of the capacito a distance = fom the cente? Poblems Chapte 32 Page 1 of 2

42 Poblem 5: Conside the situation illustated in the figue. A unifom electic field points in the z diection (out of the pape) with a value given by E z (t)=a - bt, whee a = 18 V/m and b = 9 V/(m s) and is confined to a cicula aea with a adius = 4 metes. What is the magnitude and diection of the magnetic field (in picotesla) at a point P on the cicumfeence of the cicle at the time t = 2 seconds? z-out Poblem 6: Conside the situation illustated in the Figue. A unifom electic field points in the z diection (out of the pape) with a value given by E z (t) =Asinωt, whee A = 90 V/m and ω =1,000 adians/sec and is confined to a cicula aea with a adius = 2 metes. What is the maximum magnitude of the magnetic field (in picotesla) at a point P on the cicumfeence of the cicle? z-out Poblem 7: Conside the situation illustated in the Figue. A unifom electic field points in the z-diection (out of the pape) with a value given by E z (t) = at, and a unifom magnetic field points in the z-diection with a value given by B z (t) = bt. Both fields ae confined to a cicula egion with a adius. If a = 1 V/(m s) and b = 1 T/s and if the magnitude of the induced z-out electic field at the point P on the cicumfeence of the cicle at the time t = 2 seconds is 9,000 V/m, what is the magnitude induced magnetic field (in picotesla) at the point P at the time t = 2 seconds? P Poblems Chapte 32 Page 2 of 2

43 Chapte 33 Poblems Poblem 1: If the total enegy in an C cicuit is 5.0 micojoules and =25 millih, then what is the maximum cuent (in millia)? Poblem 2: A 10 micof capacito with an initial chage Q 0 is connected acoss an 8 millih inducto. If the cicuit is completed at time t = 0, how soon (in millisec) aftewad will the chage on the capacito evese sign and become equal to -Q 0? Poblem 3: A chaged capacito is connected acoss an inducto to fom an C cicuit. When the chage on the capacito is 0.1 C the cuent is 0.5 Amps. If it the peiod of the C oscillations is 2 seconds what is the maximum chage on the capacito (in C)? Poblem 4: A cuent flows in an C cicuit with = 50 millih and C = 4 micof. Stating fom when the cuent is maximum, how long will it take (in millisec) fo the capacto to become fully chaged? Poblem 5: A 1 millifaad capacito with an initial chage Q 0 is connected acoss a 9 milliheny inducto to fom an C cicuit. If the cicuit is completed at time t = 0, how soon (in millisec) aftewad will the chage on the capacito decease to one-half of its initial value? Poblems Chapte 33 Page 1 of 2

44 Poblem 6: In the pevious poblem, if the maximum cuent is 3 milliamps what is Q 0 (in micoc)? Poblem 7: A capacito (C=8 millifaads) initially chaged by connecting it to a 2 Volt battey is connected to an inducto (=2 milliheny) to fom an C cicuit (the esistance of the cicuit is negligible). Duing subsequent oscillations, what is the maximum enegy stoed in the magnetic field of the inducto (in millijoules)? Poblem 8: A capacito C and an inducto fom an C cicuit as shown in the Figue. At a cetain instant of time when the cuent I = 2 Amps the chage on the capacito is Q = 0.01 C. A shot time late when the cuent I = 1 Amps the chage on the capacito is Q = 0.02 C. What is the fequency of the oscillations (in Hz)? C I Q Poblems Chapte 33 Page 2 of 2

45 Chapte 34 Poblems Poblem 1: The electic field component of an electomagnetic wave taveling in a vacuum is given by E y = E 0 sin (kx -ωt), whee E 0 = 300 V/m and k=10 7 /m. What ae the fequency of the oscillations (in Hz) and the diection of popagation? Poblem 2: What is the value of the z-component of the magnetic field (in micot) of the electomagnetic wave in the pevious poblem at x = 0 and t = 5.25x10-16 seconds? Poblem 3: The electic field component of an electomagnetic plane wave taveling in a vacuum is given by E = E sin( kx t) yˆ 0 + ω, whee E 0 = 300 V/m and k = 1.25x10 7 /m. What is the magnetic field component of the electomagnetic wave? Poblem 4: What is the fequency of the electomagnetic wave in the pevious poblem (in Hz)? Poblem 5: How much foce (in micon) will the electomagnetic wave in the pevious poblem exet on one squae mete of a wall when it hits the wall (nomal to the suface) and is completely eflected? Poblems Chapte 34 Page 1 of 7

46 Poblem 6: If the amplitude of the electic field oscillations 6 metes fom a point souce of electomagnetic adiation is 10 V/m, what is the powe output of the souce (in Watts)? Poblem 7: What is the amplitude of the electic field oscillations (in V/m) 2 metes fom a 60 Watt point souce of electomagnetic adiation (assume the adiation is a plane wave)? Poblem 8: ight fom a distant point souce of electomagnetic adiation exets a adiation pessue of one micon pe mete squaed when it is completely absobed by the suface S. What is the maximum value of the magnetic field (in micot) within the adiation at S? Poblem 9: ight with an intensity of 1.2 kw/m 2 falls nomally on a suface with an aea of 1 m 2 and is completely eflected. The foce of the adiation on the suface (in micon) is Poblem 10: A adio station delives 75 MegaWatts of powe which is distibuted unifomly in all diections to the adio waves. What is the adiation pessue exeted by these waves (in MicoPascals) upon a flat, pefect absobe placed pependicula to these waves a distance of 10 metes fom the tansmitte? (Note: 1 Pa = 1 N/m 2 ) Poblems Chapte 34 Page 2 of 7

47 Poblem 11: The sun has a mass of 1.99x10 30 kg and a adiation powe of 3.9x10 26 Watts. What is the maximum sola adiation foce (in N) on a pefectly eflecting squae piece of foil with sides of length = 1 mete located one million miles fom the sun (Note: 1 mile = 1,609 metes)? Poblem 12: The sun has a mass of 1.99x10 30 kg and a adiation powe of 3.90x10 26 Watts. A spaceship might be popelled in ou sola system by the adiation pessue fom the sun, using a lage sail made of foil (sailing on the sola wind). If the ship has a mass of 1,000 kg and if the sail is a pefectly eflecting squae with sides of length, what is the smallest value of (in metes) that will allow the ship to escape the sun's gavitational attaction? (The gavitational constant G = 6.67x10-11 Nm 2 /kg 2.) Poblem 13: A point souce of light is located 10 metes below the suface of a lage lake (n=1.3). What is the diamete (in m) of the lagest cicle on the pool's suface though which light coming diectly fom the souce can emege? Poblem 14: A beam of light stikes the suface of a 2-cm thick paallel-sided sheet of glass (n = 1.5) at an incident angle of 35 degees. What is the beams actual path length (in cm) though the glass? T θ 2 n=1.5 θ 1 Poblems Chapte 34 Page 3 of 7

48 θmin θc Wate n1 = 1.33 Glass n2 = 1.5 Poblem 15: A beam of light tavelling though wate (n=1.33) stikes a piece of glass (n=1.5) at an incident angle θ as shown in the Figue. What is the minimum angle θ (in degees) such that the light will not each the ai (n=1) on the othe side of the glass? Ai n3 = 1.0 Poblem 16: A beam of light tavelling though medium A at a speed of 2.25x10 8 m/s stikes medium B at an incident angle of 45 degees as shown in the Figue. If the efacted angle of the light is 30 degees, what is the speed of the light in medium B (in m/s)? 45 o A 30 o B θ0=45 o Ai A Glass B this infomation? Poblem 17: A light ay entes a ectangula glass slab at point A at an incident angle of 45 degees and then undegoes total intenal eflection at point B as shown in the Figue. What minimum value of the index of efaction of the glass can be infeed fom Poblems Chapte 34 Page 4 of 7

49 Poblem 18: A fibe optic cable (n = 1.50) is submeged in wate (n = 1.33). What is the citical angle (in degees) fo light ays to stay inside the cable? Poblem 19: A 2.0 mete long vetical pole extends fom the bottom of a swimming pool to a point 1.0 mete above the suface of the wate (n = 1.33) as shown in the Figue. If sunlight is incident 45 degees above the hoizon, what is the length of the shadow of the pole (in m) on the level bottom of the pool? ai wate 1 m 1 m 45 o Poblem 20: ight of wavelength 589 nm is incident at an angle theta on the top suface of a polystyene block (n = 1.49) as shown in the Figue. What is the maximum value of θ (in degees) fo which the efacted ay will undego total intenal eflection at the left vetical face of the block? θ 3 θ 2 θ 1 n = 1.49 Poblem 21: A light ay entes a ectangula glass slab at an incident angle of 60 degees. The glass slab has an with index of efaction n = 1.6 and a thickness T. The beam emeging fom the othe side of the glass slab is paallel to the incident beam but displaced by a distance d as shown in the Figue. What is the displacement d? T Ai d θ0=60 o Glass Poblems Chapte 34 Page 5 of 7