ELETROSTATIS::BHSE 9-4 MQ. A moving electic chage poduces A. electic field only. B. magnetic field only.. both electic field and magnetic field. D. neithe of these two fields.. both electic field and magnetic field. If the electic field at A and B ae EA and EB and the distance between them is as shown in the figue given below, then EA EB 3. If an electic cuent of ma flows though a wie, then the numbe of fee electons passing a given point in a wie pe second will be A..5 x 3. B..5 x 6...5 x 8. D..5 x. B.5 x 6 4. What is the equivalent capacitance of the following cicuit? A. 3 B...5 D. D
4. The capacitos in the given cicuit diagam have equal capacitance of each The equivalent capacitance between the points X and Y is A. 4. B. 3... D.. 5. The capacitos in the given cicuit diagam have equal capacitance of each. D The equivalent capacitance between the points X and Y is A 4. B 3.. D. D 6. The equivalent capacitance between the points A and B fom the netwok of capacitos shown below is A. μ. B. 3 μ.. 4 μ. D. μ. 7. The electic field in a egion whee the electic potential is constant thoughout is A. maximum. B. minimum.. neutal. D. zeo. A μ D zeo
ill in the blanks. Guass law elates the. field at points on a closed Gaussian suface to the. chage enclosed by the suface. (magnetic, electic, net, test) electic, net. Positon is a chaged paticle having the same as an electon. (positively, negatively, mass, symbol). positively, mass Tue o alse. Dielectic substance placed between two plates of a capacito inceases the potential enegy of the plates. alse. Dielectic substance placed between two plates deceases the potential enegy of the plates and inceases the capacitance.. A dipole in a non-unifom electic field expeiences only a toque. alse. In a non-unifom electic field, a dipole expeiences both toque and foce. It expeiences only a toque when placed in a unifom field. 3. If an electic dipole of moment p is placed nomal to the lines of foce of an electic field E, then the potential enegy of dipole is pe. alse, the potential enegy of dipole placed nomal to lines of foce is Zeo ( ie, wok done is zeo ) 4. Gauss theoem cannot be used to detemine the electic field of any suface. Tue Answe the following Questions. The electic field at a point due to a point chage is N and the electic potential at that point is V. alculate the distance of the point fom the chage and the magnitude of the chage. q V. 4 V q.5x.5m. E q 4 V 5.6x 9 E 4 9x. The tyes of aicaft ae not made of odinay ubbe (which is an insulato) but of a special ubbe which is slightly conducting. Why? The tyes of aicafts ae highly chaged duing landing due to fiction between the tyes and the ai stip (eath). If the tyes ae slightly conducting, the chage will not accumulate on them and will leak to the eath. 3. A egula pentagon of side cm has a chage 5 μ at each of its vetices. alculate the electic potential at the cente of the pentagon. V 5q 4 9 6 9x x5x5x 6 5.x V. 4. Name the factos on which capacitance of a paallel plate capacito depends. Give the coesponding elation. actos: i. Aea of the plates ii. Distance between the plates iii. Dielectic constant Relation d A KA d
V 5. Establish the fomulau, fo the potential enegy of a chaged conducto of capacitance caying a chage Q at a potential V. Small Wok done: Q dw V dq dq Total wok done: Q dw Q dq Q w QdQ w W Q w. w V [ Q V ] U V Q Q Q 6. alculate the equivalent capacitance of the netwok shown below between the points A and B, given, 3 7, 4 5 6 5. apacitos in seies 4, 5 and 6 = + + 4 5 6 = 5 3 = 5µ 3 and ae in paallel = 3 + 7µ + 5µ = µ Now, and ae in seies " = + + + + = 3 " = 4µ 7. An α-paticle is acceleated to a potential 6 volt fom the position of est. alculate its enegy in electon volt. Enegy (W) = q.v W = (e) v α-paticle = e W = x.6 x 9 x 6 J 9 6 x.6 x x J W ev = x 6 ev = MeV 9.6x
8. Obtain an expession fo potential enegy of a system of thee chages. Wok done fo moving the chage q fom infinity to the distance is qq W 4 Wok done fo moving the chage q 3 fom infinity to distance 3 and 3 is qq 3 W3 4 3 qq 3 W3 4 3 Total wok done to assemble the system is W W W W = 3 3 qq q q q q 4 4 4 3 3 3 3 qq qq 3 qq 3 4 3 3 9. An electic chage is unifomly distibuted on the suface of a hollow sphee. State how the values of electic intensity E and potential V vay inside and outside the sphee. i. Inside the sphee E = and V emains same ii. Outside the sphee E and V deceases as it moves away fom the sphee. E deceases at a faste ate.. State one essential popety of a Gaussian suface and its use. The Gaussian suface should pass though the point at which the electic field is equied.it is used to complete the electic field intensities due to cetain chage system o chaged bodies.. Thee capacitos of,3 and 6 ae connected in seies to a volt d.c supply. alculate the total enegy stoed in the capacitos. Total capacitance, 3 = = 3 6 3 6 6 6 Enegy E = v 6 () 5 OR.5Joules
. With the help of a sketch diagam, deduce oulomb s law fom Gauss theoem By Gauss theoem, q EdS o complete Gaussian suface, ds 4 E(4 ) E 4 q q If = q is the test chage placed at P, the foce between the chages =q and =q will be = q E q qq q 4 4 3. On moving away fom a point chage, the electic field due to the chage deceases. This is also tue fo a small electic dipole. Does the electic field decease at the same ate in both the cases? Give easons. No. The field due to electic dipole deceases moe apidly as E but the field due to a 3 point chage deceases less apidly as E. 4. X and Y ae two hollow concentic sphees enclosing chage Q and 3Q espectively as shown in the diagam given below. What is the atio of the electic flux though X and Y? Electic flux though X, Ratio = φ x = φ y Q ε 5Q ε = 5 Q φ x = Electic flux though Y, y ε 5Q φ= ε o
9 9 9 9 5. A squae of sides m has chage of 5,, 3 and 6 at its cones. ind the potential at the cente of the squae. The distance of the cente fom each cone of the squae of sides m is = m. The potential at the cente due to the goup of chages q, q, q 3 and q 4 q q q3 q4 V= + + + 4πε Nm m Nm = 36 = 36 J = 36V 9-9 =9. 5++3-6 6. Define elative pemittivity. What is its unit? Relative pemittivity of a medium is defined as the atio between absolute pemittivity ( ) of the medium to the absolute pemittivity ( ) of fee space. It is a dimensionless constant so it has no unit. 7. The aea of each plate of a paallel plate capacito is 4 cm and the electic field between the plates is 6 N/. ompute the chage on each plate. εa = d Q = V εa = V d Q=ε AE - - - 4-4 6 - =8.85 N m m N = 8.85-6 8. An electic dipole is fee to move in a unifom electic field. Explain its motion when it is placed paallel and pependicula to the field. i. Paallel: The net foce as well as toque is zeo, so the dipole will not move. ii. Pependicula: A maximum toque will act on the dipole which will otate to become paallel to the electic field. 9. Deive an expession fo the electic field intensity at any point due to a plane sheet of chage of - unifom chage density σ m. Electic field at a cetain distance fom the sheet is equal in othe diections as well. E = EdA+ EdA om Gauss theoem E = q-(ii) ε A A E A A =E da+e da = EA +EA E = EA -(i) E Equating (i) and (ii) : q=ea ε q E = q = σ ε A A
. Obtain an expession fo the electic potential at a point distant fom a point chage q. What will be the potential at a point as a combined effect of seveal chages? Electic potential at point p, distance fom is the wok done in binging a test chage q fom infinity. Let it come though B to A then to p whee OB = x. The wok done in moving the test chage fom B to A, a distance dx is, dwdx qq dw 4 x Integating both side w qq dw = - dx 4πε x o w = qq dx 4πε x - - x = qq 4πε - = qq 4πε x w V= q = qq - 4πε qq w= 4πε. When a medium of dielectic constant K is intoduced between the plates of a paallel plate capacito, how do the a) capacitance and b) p.d acoss the plate change? i) apacitance incease K times. ii) P.D falls to K times qq 4πε q V = q V= 4πε The potential at a point as a combined effect of seveal chages is the algebaic sum of the potential due to individual chages. ie,v= 4πε n i= qi i. Define potential enegy of a point chage in a unifom electic field E. Wite the expession fo the potential enegy of a dipole of moment p in a unifom electic field E. The potential enegy of a point chage in an electic field is defined as the wok done in binging the point chage fom fom infinity to that point. W= -pe osθ 3. alculate the electic intensity due to a point chage μ at a point distant 4cm fom the chage. 9 6 q 9 E= E= 4πε (.4) E =.5 6 Nc -
4. A paallel plate capacito of plate aea 6cm and plate sepaation mm is connected to a d.c souce of V. alculate in S.I. unit the: a) magnitude of the unifom electic field E between the plates, b) chage density σ on any plate. Answe 5 a) E V V V 3 d m m b) E 8.85 5 7 8.85 m 5. Thee ae two identical metal sphees of exactly equal masses. One is given a positive chage and the othe an equal negative chage. Afte chaging, ae thei masses equal? Explain why. No. Positive chage has fewe electons while negative chage has moe electons. So negatively chaged metal sphee have moe mass than positively chaged metal sphee.