Solution Found!
uniform line charge ? is placed on an infinite straight
Chapter 3, Problem 10P(choose chapter or problem)
Problem 10P
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.
Questions & Answers
QUESTION:
Problem 10P
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.
ANSWER:
Solution
Step 1 of 3
In this problem, we have to find the potential in the region above the plane. Given line charge which is placed on an infinite straight wire and the given distance