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Coordinator: Saleem Rao Saturday, December 02, 2017 Page: 1 Q1. Two charge q1 = + 6.00 µc and q2 = 12.0 µc are placed at (2.00 cm, 0) and (4.00 cm, 0), repectively. If a third unknown charge q3 i to be located uch that the net force on it from charge q1 and q2 i zero, what mut be the coordinate of q3? ) (16. cm, 0) B) (14. cm, 0) C) (2.49 cm, 0) D) (0, 0) E) (6.0 cm, 0) q 3 x 2 4 q 1 = +6 q 2 = 12 F 13 = F 23 Kq 1 q 3 x 2 = Kq 2 q 3 (x + 6) 2 q 1 q 3 x 2 = q 2 q 3 (x + 6) 2 6 10 6 = x 2 12 106 (x + 6) 2 1 x 2 = 2 (x + 6) 2 x 2 + 12x + 36 = 2x 2 x 2 12x 36 = 0 x = 6 ± 6 2 = 6 + 6 2 = 14.48 Coordinate (16.48,0) Q2. Two mall metallic phere and B carry + 1.00 µc and 1.00 µc of charge, repectively, held fixed at a certain ditance without touching each other. How many electron mut be tranferred from one phere to the other to reduce the force of attraction between them by a factor of four? ) 3.13 10 12 from B to B) 3.13 10 12 from to B C) 7.23 10 12 from B to D) 7.23 10 12 from to B E) 1.71 10 11 from B to F = kqq r 2 ; F = kq q r 2 q = +1 μc q = 1 μc B r q q F 4 = kq q r 2 1 4 k qq r 2 = k q q r 2 q2 4 = (q ) 2 q = q 2 q = 0.μC = 0. 106 = 3.13 1012 1.6 109

Coordinator: Saleem Rao Saturday, December 02, 2017 Page: 2 Q3. The electric field midway between two charge of +3q and 2q i 98.0 N/C and the ditance between the charge i 20.0 cm. What i the value of the charge q? ) 2.18 10 11 C B) 4.67 10 6 C C) 1.09 10 10 C D) 1.0 10 C E).73 10 11 C +3q E 2q + - 1 2 20 cm E = E 1 + E 2 98 = K(3q) (0.1) 2 + K(2q) (0.1) 2 98 = K. q 0.01 q = 98 0.01 9 10 9 = 2.177 1011 C Q4. FIGURE 1 how four ituation in which four charged particle are evenly paced to the left and right of a central point P. The charge value are indicated. Rank the ituation according to the magnitude of the net electric field at the central point, GRETEST FIRST. Figure 1 ) 2, 4, 3, 1 B) 4, 3, then 1 and 2 tie C) 3 and 4 tie, then 1 and 2 tie D) 4, 3, 1, 2 E) 1,4, 3, 2

Coordinator: Saleem Rao Saturday, December 02, 2017 Page: 3 Q. t ome intant the velocity component of an electron moving between two parallel plate are v x 1. 10 m/ and v y 3.0 10 m/. The uniform electric field between the plate i E (1.2 j ) N / C. In unit vector notation find the velocity of the electron after 2.0 µ. (ignore the effect of gravity) ) 1. 10 i 1.2 10 j m/ B) 1. 10 i 7.2 10 j m/ C).7 10 i 1.2 10 j m/ D) 1.2 10 i 1.2 10 j m/ E) 1. 10 i 3.0 10 j m/ v x = 1. 10 m will remain the ame Electric filed i upward therefoe electron will deaccelerate a y = qe = 1.6 1019 1.2 m e 9.11 10 31 = 2.107 10 11 m 2 V = U + at V = 3 10 2.107 10 11 (2 10 6 ) = 12114.8 = 1.21 10 (j ) m Q6. n electric dipole i placed in a uniform electric field E (4000 i ) N / C. What i the change in dipole' potential energy if the initial and the final electric dipole moment p and p repectively, are given by i f 30 30 p (3.72 10 i i 4.96 10 j) C. m 30 p (6.20 10 f i) C. m U = P E ) 9.92 10 27 J B) +1.4 10 27 J C) +3.97 10 26 J D) +9.92 10 27 J E) 3.97 10 26 J U = U f U i = P f E (P i E ) = [3.72 10 30 4000] + [6.2 10 30 4000] = +1.488 10 26 2.48 10 26 = 9.92 10 27 J

Coordinator: Saleem Rao Saturday, December 02, 2017 Page: 4 Q7. Conider a cloed triangular box reting within a horizontal electric field of magnitude E = 7.80 10 4 N/C, a hown in FIGURE 2. Calculate the electric flux through the lanted urface. Figure 2 ) 2.34 10 3 N.m 2 /C B) 1.17 10 3 N.m 2 /C C) 4.34 10 3 N.m 2 /C D) 7.34 10 3 N.m 2 /C E) 1.6 10 3 N.m 2 /C Φ = E = E co0 = E = 7.8 10 4 0.1 0.3 = 2340 N. m 2 C Q8. long, traight wire ha a linear charge denity λ = 7.8 nc/m. The wire i encloed by a coaxial, thin-walled non-conducting cylindrical hell of radiu 2.0 cm, a hown FIGURE 3. Find the urface charge denity σ, on the outer urface of the hell that make the net electric field zero outide the hell. ) 6.21 10 8 C/m 2 B) 3.82 10 8 C/m 2 C) 1.24 10 8 C/m 2 D) 9.37 10 8 C/m 2 E).31 10 8 C/m 2 E line = E Shell σ λ Figure 3 2.0 cm E line = For Shell λ 2πε o r E hell da = 1 ε o q enc E hell 2πr l = 1 ε o (σ 2πrl) E hell = σ ε o σ = λ 7.8 109 σ = ε o 2πε o r 2π 0.02 = 6.207 108 C m 2

Coordinator: Saleem Rao Saturday, December 02, 2017 Page: Q9. FIGURE 4 how, in cro ection, three infinity large non-conducting heet with uniform charge denitie σ1 = +3.0 µc/m 2, σ2 = +.0 µc/m 2, and σ3 = 7.0 µc/m 2, and L = 2. cm. In unit vector notation, what i the net electric field at point P? Figure 4 ) B) C) D) E) (.6 10 j) N / C 4 ( 6.8 10 j) N / C (.6 10 j) N / C 4 ( 6.8 10 j) N / C ( 1.1 10 j) N / C E net = E 1 + E 2 E 3 = σ 1 + σ 2 σ 3 = 1 [σ 1 + σ 2 σ 3 ] = 1 [3 + 7] 10 6 = 1 10 6 =.6497 10 4 N C j Q10. olid conducting phere of radiu a carrie a net charge of +2Q. conducting pherical hell of inner radiu b and outer radiu c i concentric with the olid phere and carrie a net charge Q a hown in FIGURE. rrange the electric field in four region labeled 1, 2, 3, and 4, GRETEST FIRST. ) 2, 4 then 1 and 3 tie B) 1, 2, 3, 4 C) 2, 3, 4, 1 D) 1, 3, 2, 4 E) 4 and 2 tie, then 3, 1 Figure

Coordinator: Saleem Rao Saturday, December 02, 2017 Page: 6 Q11. Work done by the electric field in moving a charge q = 4.0 mc from point to point B i +20 mj. What i the potential difference between point and B, i.e. VB V=? ) +.0 V B).0 V C) 20 V D) +20 V E) 4.0 V + + + + B V = W q = 20 103 4 10 3 = V Q12. FIGURE 6 how four arrangement of charged particle (where q 0 ), all located at the ame ditance from the origin. Rank the ituation according to the net electric potential at the origin, MOST POSITIVE FIRST (take the potential to be zero at infinity). Figure 6 ) b then a, c, and d all tie B) d, a, b, c C) a and b tie then c and d tie D) d, c, a, b E) c, b, a, d

Coordinator: Saleem Rao Saturday, December 02, 2017 Page: 7 Q13. The electric potential in xy plane i given by V 2.0 x 2 3.0 y 2, where V i in volt and x and y are in meter. In unit vector notation, what i the electric field at point.0 m,7.0 m? ) i B) i C) i D) i E) i 20 42 j V / m 20 42 j V / m 0 9 j V / m 20 9 j V / m 30 42 j V / m E x = dv = 4x = 4() = 20i dx E y = dv = [6y] = 6(7) = 42j dy = (20i + 42j ) N C or V m Q14. Two charge each of +2.0 µc are fixed along the x axi at x = 0.40 m and x = +0.40 m, a hown in FIGURE 7. third charge q = +4.0 µc i releaed from ret from y = 0.3 m. Find the maximum kinetic energy attained by the third charge after the releae. ) 0.29 J B) 0.4 J C) 0.24 J D) 0.73 J E) 0.13 J Figure 7 U = k2 106 4 10 6 0. + k 2 106 4 10 6 0. 1 2 mv2 = 2 9 109 8 10 12 = 0.288 J 0.

Coordinator: Saleem Rao Saturday, December 02, 2017 Page: 8 Q1. n air filled parallel plate capacitor i charged to a potential difference of 10 V and then diconnected from the battery. Now if you fill the pace between the plate with dielectric material of k = 2, which of the following tatement i correct ) The voltage acro the capacitor reduce to.0 V. B) The voltage acro the capacitor remain at 10 V. C) The capacitance remain the ame. D) The energy tored by the capacitor remain the ame. E) The charge tored reduce to half of it initial value. Q16. If C = 0.0 µf in FIGURE 8, what i the equivalent capacitance between point and D? ) 42.3 µf B) 32 µf C) 9.1 µf D) 28.3 µf E) 13.7 µf Figure 8 1 C 12 = 1 2C + 1 6C = 3 + 1 6C 1 = 4 C 12 6C C 12 = 3 2 C C 123 = 3 C + 4C 2 C 123 = 11 2 C C 1234 = 1 C + 1 11 C 2 = 1 C + 2 11C = 11 + 2 11 C C 1234 = 11 11 C = 0μF = 42.3μF 13 13

Coordinator: Saleem Rao Saturday, December 02, 2017 Page: 9 Q17. In FIGURE 9, the capacitor C1 = 2.0 µf and C2 = 4.0 µf. The capacitor C1 i charged to a potential difference of 10 V and C2 i initially uncharged. fter cloing the witch S, find the total energy tored by the two capacitor. ) 3.3 10 J B) 1.0 10 4 J C) 3.0 10 4 J D) 1. 10 J E).0 10 J Q 1 = C 1 V = 2 10 6 10 = 20μC Figure 9 Q T = Q 1 = 20μC Q18. E T = 1 q 2 = 1 (20 10 6 ) 2 2 C T 2 6 10 6 = 3.33 10 J n air filled parallel plate capacitor ha capacitance of C = 20.0 µf. If lower half of the capacitor i filled with dielectric material κ = 10, a hown in FIGURE 10, find the capacitance of the new capacitor. Figure 10 ) 110 µf B) 9.09 µf C) 440 µf D) 73. µf E) 173 µf C = 20μF = ε 0 d C T = C 1 + C 2 = ε 2 0 d + kε 0 = 1 2 ε 0 d + k 2 ε 0 d 2 d = 1 2 20 + 10 2 (20) = 10 + 100 = 110μF

Coordinator: Saleem Rao Saturday, December 02, 2017 Page: 10 Q19. When 11 V i applied acro a 10 m long wire with a 0.30 mm radiu, the magnitude of the current denity i 1.4 10 8 /m 2. Find the reitivity of the wire. ) 8.21 10 8 Ω.m B) 9.33 10 7 Ω.m C).72 10 8 Ω.m D) 2.38 10 8 Ω.m E) 4.16 10 8 Ω.m V = IR V = I ρ l V = I ρ l V = J ρ l 11 = 1.4 10 8 ρ 10 ρ = 11 1.4 10 8 10 = 8.214 108 Ω m Q20. heater element with potential difference of 400 V acro it tranfer electrical energy to thermal energy at the rate of 3000 W. t what rate the heater will tranfer the energy if it i connected acro a potential difference 300 V. P = V2 R ) 1.69 kw B) 2.2 kw C) 3.7 kw D) 1.13 kw E) 2.92 kw R = (400)2 3000 = 3.333 P = (300)2 3.33 = 1.687 103 W = 1.69 kw