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NAME: EAD 234A: E&M Midterm Thursday, 2/11/2010 Note: (1) You may use Jackson and a dictionary, but calculators and lecture notes are NOT allowed. (2) You may use any equation in Jackson without derivation unless you are specifically asked to derive it.

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(1) A uniform line charge density λ is placed on an infinite straight wire, a distance d above a grounded conducting plane. (For definiteness, assume the wire runs parallel to the x-axis and directly above it, and the conducting plane is the x-y plane.) (a) Find the potential in the region above the plane. (b) Find the surface charge density σ induced on the conducting plane. Solution: (a) Use image charges Field around one wire: Gaussian cylindrical surface: () () () 00 2 0 ˆ ˆ 2 encl L Q L Ed a Symmetry E E s s L d z dsEs s LEs π λ εε φπ ε == ⇒= = ∫∫ G G G G w The lids don’t contribute because ˆ 0 sd a = G there.
() 0 2 Es s λ πε ⇒= () () 0 00 ln 2 s s s Vs d s s = Here, s denotes the (shortest) distance from the wire. So, for a wire that runs parallel to the x-axis

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