[malik (OP)]

 A grounded, infinite circular cylindrical conductor of radius a lies in a previously uniform electric field,
with its axis perpendicular to E0 as in the figure.
a. Show that V = - E0 (1 ­- a2/ ρ2)ρcosφ satisfies Laplace's equation.
b. Find E at ρ2 >> a2 and at ρ= 0. Do those values make sense?

[diagram=352_0]

[malik (OP)]

by using this equation

V(r,θ) = ∑ [Al r^l + Bl r^-(l+1)] Pl(cos θ) where last term is legender polynomial.

this is the  general solution of Laplace equation in spherical coordinate.

[syhprum]

I see we correspondents are being weighed in the balance and found wanting, I rather thought this forum was for the amateur enthusiast and not for a source of information on such esoteric subjects

[graham.d]

Life's too short to be solving someone's homework problems :-)

Try this site:

http://web.mit.edu/6.013_book/www/book.html

and read chapter 5