We know that the charge on a conductor goes to the surface. but just how it dist

Question

We know that the charge on a conductor goes to the surface. but just how it distributes itself there is not easy to determine. One famous example in which the surface charge density can be calculated explicitly is the ellipsoid: x2/a2+y2/b2+z2/c2 = 1 In this case11 sigma = q/4piabc (x2/a4+y2/b4+z2/c4)-1/2 where Q is the total charge. By choosing appropriate values for a. b, and c. obtain (from Eq. 2.57): the net (both sides) surface charge density sigma(r) on an circular disk of radius K the net surface charge density sigma(r) on an infinite conducting "ribbon" in the x y plane, which straddles the y axis from x = -a to x = a (let Delta be the total charge per unit length of ribbon); the net charge per unit length lambda(x) on a conducting "needle", running from x = -a to x = a. In each case, sketch the graph of your result.

Explanation / Answer

(a)

surface charge density is conventionally given the symbol sigma

for a circular disk, we have the relationship

sigma = Q / pi r2

(b)

if Q is the net charge pere unit length then

sigma(x) = Q / sqrt(a2 - x2)

(c)

in case of conducting needle running from x = - a to x = + a

sigma = Q / 2a

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