matschek (ccm2548) Ch17-h3 chiu (57890) 1

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1 matshek m2548) Ch17-h3 hiu 5789) 1 This pint-out should have 16 questions. Multiple-hoie questions may ontinue on the next olumn o page find all hoies efoe answeing points A student said, The eleti field at the ente of a haged spheial shell is zeo, so the potential at that loation must e zeo. Is this statement tue o false? 1. Tue 2. False 2 1. points The enegy density inside a etain apaito is 14 J/m 3. What is the magnitude of the eleti field inside the apaito? Note that ǫ = C 2 N 1 m 2. Answe in units of N/C 3 1. points Conside two isolated spheial ondutos, eah having net hage Q. The sphees have adii a and, whee > a. potential diffeene of V 1i. A seond paallel plate apaito is initially unhaged, has an aea A 2 and a gap of length s 2 filled with plasti whose dieleti onstant is κ. Connet a wie fom the positive plate of the fist apaito to one of the plates of the seond apaito and onnet anothe one fom the negative plate of the fist apaito to the othe plate of the seond apaito. The initial voltage of the fist apaito efoe onnetion is given y V 1i. Denote the final potential diffeenes of the fist and the seond apaitos to e V 1f and V 2f espetively and the final field in the gap the seond apaito in pesene of the dieleti e E 2f. Afte the onnetion, let the hage aosstheseondapaitoedenotedyq 2. Conside the following statements: Ia. V 1f = V 2f I. V 1f > V 2f IIa. E 2f = 1 Q 2 ǫ κ II. E 2f = 1 2ǫ κ A 2 Q 2 A 2 Q a Q IIIa. V 2f = 2E 2f s 2 III. V 2f = E 2f s 2 1. Ia, II, III Whih sphee has the highe eleti potential at its sufae? Assume that the potential at is zeo. Also assume the two sphees ae fa apat and neglet the effet on one sphee due to the othe sphee. 1. Both sphees have the same potential. 2. The sphee of adius a 3. The sphee of adius 4 pat 1 of 2) 5. points An isolated paallel plate apaito of aea A 1 with an ai gap of s 1 is haged up to a 2. I, II, IIIa 3. I, IIa, IIIa 4. I, II, III 5. Ia, IIa, IIIa 6. Ia, II, IIIa 7. Ia, IIa, III 8. I, IIa, III 5 pat 2 of 2) 5. points Fo this pat of the polem, we will simplify

2 matshek m2548) Ch17-h3 hiu 5789) 2 the polem assuming that the two apaitos have idential geomety, i.e. A 1 = A 2 = A and s 1 = s 2 = s. Thee is still the dieleti sla with dieleti onstant κ in apaito 2. Befoe the onnetion let the initial voltage of the fist apaito y V 1i. Denote the final potential diffeenes of the fist and the seond apaito to e V 1f and V 2f. Afte the onnetion, let the hage aoss the seond apaito e denoted y Q 2. Conside the following statements: Ia. V 1f = V 2f I. V 1f > V 2f IIa. E 2f = 1 Q 2 ǫ κ A II. E 2f = 1 2ǫ κ Q 2 A IIIa. V 1f = κ 1+κ V 1i III. V 2f = 1 1+κ V 1i 1. Ia, II, IIIa 2. I, IIa, IIIa 3. I, II, IIIa 4. I, II, III 5. I, IIa, III 6. Ia, IIa, III 7. Ia, II, III 8. Ia, IIa, IIIa 6 pat 1 of 2) 5. points Conside a paallel plate apaito whee the hage on the plate is Q and the plate aea is A. One plate is fixed and the othe plate is pulled y a foe F whih maintains an equiliium with a gap width d. Detemine the magnitude of the foe. 1. Q 4d 2 ǫ ) Q 2. Q 3. Q 2d 2 ǫ 4. Q Q 6. 2Q d 2 ǫ 7. Q 4 8. Q d 2 ǫ 7 pat 2 of 2) 5. points Now slowly inease the gap width y a distane s. Find the inease of the enegy in the apaito system U. Hint: onside only the eleti field that exets a foe on the moile plate.) 1. Q d 2 ) QA 2. Q s ǫ A 3. Q d+ s) ǫ 4. Q d 5. Q d+ s) 6. Q s 2 7. Q d+ s) 2 8. Q s A 9. Q d+ s) 2ǫ A 1. Q s 2ǫ

3 matshek m2548) Ch17-h3 hiu 5789) 3 8 pat 1 of 2) 5. points The hage distiution shown in the figue is efeed to as a linea quadupole. Y +Q 2Q +Q X d, ) +d, ) Find the exat expession fo the potential at a point on the x axis whee x > d, whee the potential to e zeo at infinity V x = kq x+d 1 x + 2 ) 2 2. V x = kq x+d + 1 x + 2 ) 3. None of these 2 4. V x = kq x+d + 1 x 2 ) 5. V x = kq x 6. V x = kq x+d + 2 x 1 ) 7. V x = kq x+d 2 x 1 ) 8. V x = kq x+d 2 x + 1 ) 9. V x = kq x+d + 2 x + 1 ) 2 1. V x = kq x+d 1 x 2 ) 9 pat 2 of 2) 5. points Appoximate the potential when x d. 1 1±ǫ 1 ǫ+ǫ2 ǫ 3 +, and 1+ǫ) n 1+nǫ+ fo ǫ V x = Qd2 kx 3 2. V x = 2kQd2 x 3 3. V x = 2kQx2 d 3 4. V x = 2kQd x 5. V x = 4kQd2 x 3 6. V x = 4kQd2 x 3 d 3 7. V x = 2kQd2 x 8. V x = 2kQd2 x 2 9. V x = 2kQ x 2 1. V x = kqx2 d 3 1 pat 1 of 2) 5. points Conside a system of a metalli all with net hage q 1 and adius enlosed y a spheially symmeti metalli shell with net hage q 2, inne adius 2 and oute adius 3. If q 2 is the hage on the outside sufae of the shell and q 2 the hage on its inside sufae, then q 2 +q 2 = q q 2 q 1 O B q 2 C q 2 Find the potential at C. OB = and OC =. 1. V C 2. V C = 2 k q V C 3 2

4 matshek m2548) Ch17-h3 hiu 5789) 4 4. V C = k q 2 5. V C 3 6. V C = k q 1 7. V C = 2k q 1 8. V C 3 2 M. 9. V C = k q 1 q V C 11 pat 2 of 2) 5. points Detemine the potential at B. 1. V B 3 2 P. 2. V B 3. V B = k q 2 4. V B = 2 k q 2 5. V B = 2 k q 1 6. V B = k q 1 q G. 7. V B = k q 1 8. V B 3 9. V B V B. 12 pat 1 of 2) 5. points Consideaspheewithadiusandhage Q and the gaphs S. Whih diagam desies the V) funtion eleti potential vs adial distane) fo a onduting sphee? 1. P

matshek m2548) Ch17-h3 hiu 5789) 5 2. G 3. 4. M 5. S 13 pat 2 of 2) 5. points Whih diagam desies the V) funtion eleti potential vs adial distane) fo a unifomly haged non-onduting sphee? 1. S 2. G 3. 4. M 5. P 5.

5 matshek m2548) Ch17-h3 hiu 5789) 5 2. G M 5. S 13 pat 2 of 2) 5. points Whih diagam desies the V) funtion eleti potential vs adial distane) fo a unifomly haged non-onduting sphee? 1. S 2. G M 5. P 5. V = 2 kq 6. V = ) kq 7. V = 2 2 kq 8. V = kq 9. V = 2 2 kq2 1. V = ) kq 2 15 pat 1 of 2) 5. points When a dieleti is pesent in a haged apaito, the dieleti is polaized. The figue elow shows a simple model: a laye of polaized hage foms at the uppe and lowe sufaes of the dieleti, leading to a edution of the effetive plate hage and a edued field E points Thee point hages, eah of magnitude q, ae plaed at 3 ones of a squae with sides of length. The hage fathest fom the empty one is negative q) and the othe two hages ae positive +q). + A O + B What is the potential at point A? 1. V = 2 1 ) kq V = 2 kq 2 3. V = 2 2 kq 2 4. V = 2 kq2 In eality, eah individual moleule of the dieleti is polaized, eoming a dipole see the illustation Fig in M&I v.ii). The sum of the dipole ontiutions gives the eleti field due to the polaization of the dieleti E pol. The simple model shown aove is justified y assuming that the effets of the polaized hages in the inteio of the dieleti lagely anel, leaving only the outemost laye of dipole hage at the top and ottom sufaes to ontiute. Given a dieleti onstant κ, plate hage Q, and plate aea A, detemine the magnitude of the polaized hage Q pol.

6 { Hint: within the dieleti, E = Q/A) }. κǫ ) κ 1 1. Q κ+1 2. Qκ 1) 3. κq 4. Q 1 1 ) κ 5. Q 1+ 1 ) κ matshek m2548) Ch17-h3 hiu 5789) 6 6. Q κ 16 pat 2 of 2) 5. points The apaitane of a paallel plate apaito in fee spae is given y C = Q V = Q A ) = ǫ Q/A)d d, ǫ whee V is the potential diffeene aoss the gap. When the gap is filled withamedium of dieleti onstant κ, the eleti field is edued fom its fee-spae value E to E = E/κ. Detemine V and C, the potential diffeene and apaitane in the pesene of the dieleti. 1. V = κv, C = κc 2. V = κv, C = C κ 3. V = V κ, C = C κ 4. V = V κ, C = κc

AVS fiziks. Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES

AVS fiziks. Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES ELECTROMAGNETIC THEORY SOLUTIONS GATE- Q. An insulating sphee of adius a aies a hage density a os ; a. The leading ode tem fo the eleti field at a distane d, fa away fom the hage distibution, is popotional