110Amid1+solns

# 110Amid1+solns - R θ = V(3 cos 2 θ − 1 where V is a...

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Unformatted text preview: R, θ ) = V (3 cos 2 ( θ ) − 1), where V is a constant. Calculate the potential inside the sphere as a function of position r and angle θ . 5. (30 points) Two semi in²nite grounded conducting regions meet at right angles. In the region between them, there is a point charge q , at a position ( a, b ), situated as shown below. The grey region is conductor and at potential V = 0. The conductor extends in²nitely both into and out of the page. Set up the image con²guration and calculate the potential in this region without conductor. y x V=0 a b q Additional Information: P ( x ) = 0 , P 1 ( x ) = x, P 2 ( x ) = 3 x 2 − 1 2 , P 3 ( x ) = 5 x 3 − 3 x 2 Basic equations for electrostatics: F = q E , ∇ · E = ρ ǫ , E = −∇ V, ∇ × E = 0 In spherical coordinates ∇ 2 V = 1 r 2 ∂ ∂r ( r 2 ∂V ∂r ) + 1 r 2 sin θ ∂ ∂θ (sin θ ∂V ∂θ ) + 1 r 2 sin 2 θ ∂ 2 V ∂φ 2 ....
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110Amid1+solns - R θ = V(3 cos 2 θ − 1 where V is a...

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