Solution Homework PHY Midterm

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1 Solution Homework PHY3--53 Midterm. Three eual charges, each of +4.6 µc, are spaced along a straight line. Charge A, is at one end of the line of.8 m from the central charge, B. Charge C is the other side of charge B a distance of. m from charge B. What is the magnitude and direction of the total force on each charge? Solution: At point A k B A BA rba ( (4.6 (.8 ( r 5.88 ( iˆ BA k C A CA rca ( (4.6 (4 (4.6. r. ( iˆ CA v v r CA ( 5.88 iˆ + (. iˆ 7.7 iˆ A BA + ASWER At point B: k A B AB rab ( (4.6 (.8 ( r 5.88 BA iˆ PHY3

2 Solution Homework PHY3--53 Midterm k C B CB rcb ( (4.6 (. ( r 3.3 ( iˆ CB v v r CB (5.88 iˆ ( 3.3 iˆ.5 iˆ B AB + + ASWER At point C: k A C AC rac ( (4.6 (4 (4.6. r. BA k iˆ ( (4.6 B C BC rbc (. ( r 3.3 v BC B AB + iˆ v r CB (. iˆ (3.3 iˆ 5. + ASWER PHY3

3 Solution Homework PHY3--53 Midterm. In the Bohr theor of the hdrogen atom, an electron moves in a circular orbit about a proton, where the radius of the orbit is.5 - m. (a. ind the electric force eerted on each particle. Solution: given (proton.6 C, (electron.6 C k r ( (.6 (.5 ( (b If this force causes the centripetal acceleration of the electron, what is the speed of the electron? Solution: ( from mv r C m electron. -3 kg 8. mv C r (. ( v m 8 (8. (.5 v 3.. m / s 6 PHY3

4 Solution Homework PHY3--53 Midterm 3. ind the force eerted on point charge a b the other two point charges depicted in the diagram: Solution: At point A ca sin3 o ca ca cos3 o 3 ba kba ( (4(3 ba.73 o rba (.5sin 3 r ba.73 ( ˆj k ( (5(3 5.4 c a ca rca (.5 r ca ca o cos3 ( iˆ + ca sin ( ˆ i ( ˆj iˆ ˆj v v r a ba + ca (.73 ˆ j + ˆ ( 4.67 i +.7 ˆj iˆ ˆj Magnitude Direction ˆj a ( ( ASWER.46 o θ tan ( PHY3

5 Solution Homework PHY3--53 Midterm Solution: At point B ab cb k ( a b ab o rab (.5sin 3 r.73 ab k ˆj ( c b cb o rcb (.5cos3 (3(4.73 (5(4.6 r cb.6 iˆ v v r b ab + cb.73 ˆ j +.6 iˆ.6 iˆ +.73 ˆj Magnitude Direction b (.6 + (.73.8 ASWER.73 o θ tan ( Solution: At point C ac cos3 o bc ac sin3 o ac k b c bc rbc ( (4(5 (.5cos3 o.6 PHY3

6 Solution Homework PHY3--53 Midterm r bc.6 ( iˆ k ( a c ac rac (.5 ac (3(5 5.4 r o cos3 (ˆ i + sin 3 ( ˆj ac ( ˆ i 5.4 ( ˆj iˆ ˆj v v r c bc + ac (.6 ˆ i 4.67 iˆ.7 iˆ ˆj ac +( j ASWER ˆ PHY3

7 Solution Homework PHY3--53 Midterm 4. Consider a thin spherical shell of radius 4. cm with a total charge of 3. µc distributed uniforml on its surface. ind the electric field. (a.. cm from the center of the charge. (b.. cm from the center of the charge. (a. cm Solution net in + + Guass s law + r + E v. da v + + (4 r net ε E π + + E (b. cm + net 3 C + + Guass s law + r + E v. da v + + E(4π r E E 3. E 4(3.4(. (8.85 net ε ε 4πr ε 7. / C 6 PHY3

8 Solution Homework PHY3--53 Midterm 5. A long straight metal rod has a radius of 5. cm and a charge per unit length of 3 nc/m. ind the electric field (a. 3. cm (b.. cm and (c.. cm from the ais of the rod, where distances are measured perpendicular to the rod. (a. 3. cm Solution : E v. da v E, net ε (b.. cm Solution : EdA cos E v. da v + EdA cos + EdA 3 cos EA A πrl is area the a side of clinder. net ε λl ε λl ε E λ πrε E λ πrε 3 C (3.4(.( / C 3 (c. cm Solution : E λ πrε 3 C (3.4(.( / C PHY3

9 Solution Homework PHY3--53 Midterm 6. A proton accelerates from rest in a uniform electric field of 64/C. At one later moment, its speed is. Mm/s (a. find the acceleration of the proton. Solution a E m (64 / C(.6 (.67 7 kg C 6.3 m / s (b. over what time interval does the proton reach this speed? 6 Solution given: v. m / s, u, a 6.3 m / s v u + at 6. + (6.3 t 5 t.6 s (c. how far does it move in this time interval? 5 Solution given: u, a 6.3 m / s, t.6 s s ut + at 5 (6.3 (.6.77 m (d. What is its kinetic energ at the end of this interval? Solution given: v. m / s , m oton kg Pr E k mv (.67 (.. J PHY3

10 Solution Homework PHY3--53 Midterm 7. A proton moves at m/s in the horizontal direction. It enters a uniform vertical electric field with a magnitude of.6 5 /C. Ignoring an gravitational effects, find (a. the time interval reuired for the proton to travel 5. cm horizontall. 5 Solution given: u 4.5 m / s, s 5. m s t u t s u m 7. s ns s 5 (b. its vertical displacement during the time interval in which its travels 5. cm horizontall. u, a E 5 (.6 (.6 7 m (.67 kg 7 t. s s u t + a t ( 3 7. m / s (. s.57 Solution given: C. 3 m / s, m (c. the horizontal and vertical component of its velocit after it has traveled 5. cm horizontall. Solution given: v 5 u 4.5 m / s v u + a t (. m / s The resultant of velocit v 4.5 iˆ 7 (. s 5 +. / s. / 5 m s 5 ˆj m PHY3

11 Solution Homework PHY3--53 Midterm 8. Two parallel plates having charges of eual magnitude but opposite sign are separated b. cm. Each plate has a surface charge densit of 36. nc/m. A proton is released from rest at the positive plate. Determine (a. the potential difference between the plates. Solution V Ed But σ 36 E 8.85 ε / C V (467.8( V (b. the kinetic energ of the proton when it reaches the negative plate. 7 Solution : m proton.67 kg, proton.6 C.6 V rom problem (a E E Ek + V Ek + V V Ek ( V + ( V Ek -.6 ( V V Ek V ( V V V.6 (488.4 Ek 7 Ek 7.8 J (c. the speed of the proton just before it strikes the negative plate. Solution Ek mv J (.67 kg v v 3.6 m / s 5 (d. the acceleration of the proton. Solution v u + as ( ( + a(. a 3.8 m / s PHY3

12 Solution Homework PHY3--53 Midterm (e. the force on proton. Solution ma 7 6 (.67 kg(3.8 m / s 6.5 (f. rom the force, find the magnitude of the electric field and show that it is eual to the electric field found from the charge densities on the plate. Solution E E / C (.6 C The electric field in (f is the same as the electric field in (a. PHY3

13 Solution Homework PHY3--53 Midterm. Three charges, 4-6 C, - -6 C, and C are placed at the corners of an isosceles triangle with sides.3 m. What is the potential energ of the sstem? Solution k E P r k + r 3 3 k 3 + r ( (4 C( C ( +.3m ( (5 C(4 C +.44m J 3 ( C(5.3m C PHY3

14 Solution Homework PHY3--53 Midterm. A charged droplet of mass kg is hovering motionless between two parallel plates. The parallel plates create have a potential difference of 4 V and are. mm apart. What is the charge on the particle? B how man electrons is the particle deficient? E mg What is the charge on the particle Solution rom V 4V 7 E. / C 3 d. m E mg mg (5.88 kg(.8m / s 7 E. / C C 3 e.6 C / electrons elcetrons C (positive charge PHY3

15 Solution Homework PHY3--53 Midterm. A particle with a charge of -.5 uc and a mass of.5-6 kg is released from rest at point X and accelerates toward point Y, arriving there with a speed of 4 m/s. a. What is the potential difference V Y - V X between X and Y? b. Which point is at a higher potential? Solution a. What is the potential difference V Y - V X between X and Y? mv + 6 E E V mv + V 6 (.5 ( + (.5 V (.5 (4 + (.5 V.5 V V 3.5 V -V.5 47 V b. Which point is at a higher potential? V > V PHY3

16 Solution Homework PHY3--53 Midterm. A light bulb filament is made of tungsten which has a coefficient of resistivit (α of.45(c -. At room temperature of C the filament has a resistance of Ω. (a What is the average power of the light bulb immediatel after it has been plugged into a V ac outlet? V ( P 44 R W (b After a ver brief time, the light bulb filament has changed temperature and is glowing brightl, the "rms" current is measured to be.833 amp. What is the resistance of the light bulb now? V R I.833 Ω (c What is the average power of the light bulb when it is glowing brightl as in part (b? V ( P. 6 R 44.6 W (d What is the temperature of the filament when it is glowing brightl? R R ( + α T 44 ( +.45( T T T o C PHY3

17 Solution Homework PHY3--53 Midterm 3. A current of 5 amps is maintained through a batter for 3 seconds. In this time 6 J of chemical energ is transformed into electrical energ. (a What is the emf of the batter? (b What electrical power was supplied to the circuit eternal to the batter? (a. W P Iε t 6 3 s J (5ε ε 4 V (b. W 6 J P t 3s W 4. What is the potential difference between Points A and B? ind the current go through each of resistors. R AB ( 36 Ω (3 + 6 R 4 + 6Ω ε I A R 6 V IR AB AB ( 4 V V up I ( I ( + I. 33A I (5 + I. 66A 6 PHY3

18 Solution Homework PHY3--53 Midterm 5. ind the currents that go through each of resistor and loss power on 5 Ω. If s and s is switch when (a. if turn off s and s (b. if turn off s and turn on s (c. if turn off s and turn on s 4 V Ω a 5 Ω S b I V, Ω - + c S I Ω (a. if turn off s and s (วงจรเป ด กระแสไม ไหล ด งน น I I (b. if turn off s and turn on s (กระแสไม ไหลในสายกลาง ε I( 4 + I ε 4. 33A (c. if turn off s and turn on s (กระแสไม ไหลในสายล าง ε + ε I ( I. 4A PHY3

19 Solution Homework PHY3--53 Midterm 6. ε V, ε V, R R Ω and three (, (, (3 4.-W,.-V light bulbs are connected in the circuit as shown in figure. ind which bulb is the most brightness. R ( R ( (3 ε ε R bulbs V ( 5Ω P 4 R R 3 R ε I ε R4 I R 5 I z จะได ε IR Loop ; I ( + ( I I 5 45I 5I ( Loop ; I (5 + ( I I 5 + ( I I 5 z 5I + 75I 5I ( Loop 3; I ( + ( I I 5 I z z z z 5I + 45 (3 I.8A, I.4A, I z. A หลอดท : P I (5 (.4 (5. 44 W หลอดท : P ( I I 5 (.8.4 (5. 64 W หลอดท 3 : P3 ( I I z 5 (.4 (. (5. 36 W หลอดท สว างท ส ด, หลอดท สว างน อยท ส ด PHY3

20 Solution Homework PHY3--53 Midterm 7. orm this figure, Calculate the magnetic field at point P which is the center of a circular loop. R P I I R ว ธ ท า R P I I R ค ดท ลวดต วน ายาวมาก จากกฎของแอมแปร B v. dl v µ I net B dl cos µ I (Q B ก บ dl ม ท ศทางเด ยวก น B (π (R µ I B µ I ท ศพ งออกจากจ ด P 4πR ค ดท ลวดวงกลม จากกฏของบ โอต ซาวาร ต โดยท dl v ก บ rˆ ท าม ม ต อก น แทนค า µ I dl sin φ B 4π r µ I dl sin 4π r B PHY3

21 Solution Homework PHY3--53 Midterm µ I (πr 4πR I R µ ท ศพ งออกจากจ ด P สนามแม เหล กล พธ ท จ ด P B B + B µ I + 4πR I R µ ท ศพ งออกจากจ ด P ตอบ PHY3

22 Solution Homework PHY3--53 Midterm 8. The straight rod carries a current of 4 A, where there is a horizontal magnetic field with magnitude -3 T. If the length of rod is 5 cm, find the magnitude of magnetic force eerts on this rod. B IlBsinθ (4A(.5( 3 sin 3 3 o 4. In which direction, if an, will the metal rod be deflected? B. A magnetic field has a magnitude of.78t and is uniform over a circular surface that has radius of. m. The field is oriented at an angle of of ø 5 o with respect to the normal to the surface. What is the flu through the surface? φ B BAcosθ (.78T ( π (. cos 5 o. 4 Weber PHY3

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