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Phy102&amp;08-II-ms1

# Phy102&amp;08-II-ms1 - 1 The uniform electric field...

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1. The uniform electric field between two conducting charged plates shown in the figure has a magnitude of E = 28.40 N/C. The plate separation is 1 m, and we launch an electron from the bottom plate directly upward with v o = 3 × 10 6 m/s. Will the electron reach the top plate? Justify your answer by providing numerical data. * 2 12 31 19 / 10 0 . 5 10 11 . 9 40 . 28 10 6 . 1 s m m qE a y y × - = × × × - = = - - * ( ) ο ο ν ν y y a y y y - = - 2 2 2 m H H 90 . 0 10 0 . 5 2 10 9 0 12 12 = × × - = × - * Since H < 1m, the electron does not reach to the top plate. 2. Three point charges, 1 μ C each, are placed on three corners of an equilateral triangle with side a = 1 m. Write the net electric field at the middle point P, in terms of unit vectors. 2 2 2 2 75 . 0 4 m a a r = - = * C N k r q k E 12 2 3 = = and 3 3 1 1 3 2 1 E E E E E E E E r r r r r r r r = + - = + + = * C N k E E x x 4 . 10 30 cos 12 3 = × = = * C N k E E y y 0 . 6 30 sin 12 3 = × = = * ( ) ( ) j C N k i C N k E ˆ 0 . 6 ˆ 4 . 10 + = r y P a x y v o E y x a r E 1 E 2 E 3

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3. A long non-conducting cylinder with radius a = 0.5 m has a volume charge density ρ = -5 nC/m 3 . Find the magnitude of electric field (in N/C) at a distance r = 0.2 m from its axis. ο ε enc q dA E = r - = rLE dA E π 2 r LP r q enc 2 π = C N E r E 5 . 56 10 85 . 8 2 2 . 0 10 5 2 12 9 = × × × × - - = - = - - ο ε ρ 4. A very long line of charge having a uniform charge density λ is at a distance of d = 0.4 m from a positive point charge (Q = 4 μ C) as shown in the figure. If the net electric field at point A is zero, find the value of λ (sign and magnitude).
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