uniform line charge λ is placed on an infinite straight wire, a distance d above a groun...

uniform line charge λ is placed on an infinite straight wire, a distance d above a grounded conducting plane. (Let’s say the wire runs parallel to the x-axis and directly above it, and the conducting plane is the xy plane.)

(a) Find the potential in the region above the plane. [Hint: Refer to Prob. 2.52.]

(b) Find the charge density σ induced on the conducting plane.

Reference prob 2.52

For Theorem 2, show that (d)⇒(a), (a)⇒(c), (c)⇒(b), (b)⇒(c), and (c)⇒(a).

Reference Theorem 2,

Divergence-less (or “solenoidal”) fields. The following conditions are equivalent:

(a) ∇ ? F = 0 everywhere.

(b) ? F ? da is independent of surface, for any given boundary line.

(c) for any closed surface.

(d) F is the curl of some vector function: F = ∇ × A.