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Phy102&amp;07-S-final

# Phy102&amp;07-S-final - Problems Detailed solution is...

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Problems - Detailed solution is required. (Solutions) 1. Four point charges are located on the x-y-plane as shown in the figure. Given q = 1 nC, the x-component of the electric field at the origin is: 3 points a) 18.0 N/C b) 12.7 N/C c) 6.4 N/C d) 9.0 N/C e) zero E = 2 kq E x = 4Ecosθ = 2 2 2 4 kq =12,72 N/C 2. Two spheres of radii a and 2a (a < 1m) are centered on the x-axis at x = 0 m and at x = 6 m, as shown. The spheres have equal uniform surface charge densities. Where on the x- axis can a point charge Q be placed so that the net force on it is zero? 3 points a) x = 3 m b) x = –4 m c) x = 8 m d) x = 2 m e) x = – 2m q 1 = σ4πa 2 q 2 = σ4π(2a) 2 =4q 1 2 1 E E = 2 1 2 1 ) 6 ( 4 x kq x kq = 2 2 ) 6 ( 4 1 x x = m x 2 = x y -q (1m, 1m) -q (1m, -1m) q (-1m, -1m) q (-1m, 1m) a 2a x σ σ

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3. Two rods with non-uniform charge densities are located along the x and y-axis as shown in the figure. The linear charge densities are λ 1 = 3x 2 nC/m and λ 2 = – 4y 2 nC/m. The magnitude of the electric field at the origin is: 4 points a) 90 N/C b) 132 N/C c) 198 N/C d) 154 N/C e) 148 N/C 2 r dr k dE λ = C N dx m C n k x dx k dE / 27 3 2 1 1 = = = λ C N C N dx E / 54 / 2 * 27 27 4 2 1 = = = C N dx m C n k y dx k dE / 36 4 2 2 2 = = = λ C N C N dy E / 144 / 4 * 36 36 6 2 2 = = = C N E E E net / 8 . 153 2 2 2 1 = + = 4 . A sphere of radius 1m and surface charge density σ = 4 μC/m 2 is centered at the origin. The work done by the electric field on a point charge q = 1 μC that travels from point A to B is: 4 points a) – 77×10 -3 J m r A 6 . 3 3 2 2 2 = + = b) 77×10 -3 J m r B 24 . 2 1 2 2 2 = + = c) 328×10 -3 J r A d) – 328×10 -3 J r B e) zero Q= C r 6 2 10 16 4 × = π π σ ; A A r kQ V = B B r kQ V = J r r qkQ V V q
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