# The Naked Scientists Forum

### Author Topic: How does an infinite circular cylindrical conductor behave in an electric field?  (Read 3925 times)

#### malik

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• Posts: 4
##### How does an infinite circular cylindrical conductor behave in an electric field?
« on: 03/06/2008 09:54:56 »
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?

« Last Edit: 03/06/2008 14:36:01 by malik »

#### malik

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• Posts: 4
##### How does an infinite circular cylindrical conductor behave in an electric field?
« Reply #1 on: 06/06/2008 16:21:34 »

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.
« Last Edit: 07/06/2008 07:59:03 by malik »

#### syhprum

• Neilep Level Member
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##### How does an infinite circular cylindrical conductor behave in an electric field?
« Reply #2 on: 06/06/2008 19:27:50 »
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

• Neilep Level Member
• Posts: 2208
##### How does an infinite circular cylindrical conductor behave in an electric field?
« Reply #3 on: 06/06/2008 21:03:36 »
Life's too short to be solving someone's homework problems :-)

Try this site:

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