EE325_quiz_4_sol_Yilmaz

EE325_quiz_4_sol_Yilmaz - NAME I EE325-Fall 2009 Quiz 4 1...

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NAME: _________________ I EE325-Fall 2009 Quiz 4 1) Consider a uniform line charge with density l ρ and of length L centered at the origin and directed along the z -axis. Find the electric potential at the point (0,0, z ) for / 2 z L > . (Hint: ln b a dz z a z z z b = ) (5 points) /2 0 0 /2 / 2 ln V 4 4 / 2 L l l L dz z L V z z z L ρ ρ πε πε + = = 2) Given that 3 2 ˆ 10 sin A/m r θ = J a in spherical coordinates, find the current crossing the spherical shell 2 m r = . (Hint: 2 2sin 1 cos2 θ θ = − ). (5 points) 2 2 3 2 0 0 2 3 2 3 3 2 3 0 0 0 0 ( sin ) 10 sin sin 1 4 10 sin 4 10 (1 cos2 ) 4 10 ( sin 2 ) 4 10 A 2 r I d d r d d r d d d d d π π π π π π θ θ φ θ θ θ φ θ θ φ π θ θ π θ θ π = = = = × = = = ∫ ∫ ∫ ∫ J S S a i EE325-Fall 2009 Quiz 4 1) Find the electric potential at a point OB r due to the electric dipole consisting of charge +Q
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