Electric Field Equation Hollow Cylinder

n0083

Hello,
Does anyone know of (or have a link to) an equation for the electric field at any point inside a a hollow cylinder shell of finite length?

thanks,

jtbell

I've never seen one. I suspect that it's not possible to get a closed formula for all points, and that you'd have to calculate it via numerical integration or using a series approximation of some kind.

clem

More detail please. Is it a conducting cylinder kept at a given potential?
Are the ends open or closed?

n0083

Okay, let's simplify.

Suppose the cylinder is of finite length, and the point is inside the cylinder midway between the two ends. The ends are open. The charge is uniform and kept constant. The cylinder is made of conducting material.

clem

That is impossible. A conducting cylinder will not have a uniform charge.

n0083

True that.

Suppose it is made of non-conducting material such that the charge is uniformly distributed.

clem

That problem can be solved by taking the field or potential on the axis of a uniformly charged ring and integrating along the axis.

jtbell

Right, on the axis you can get an equation for the field as a function of position fairly easily. Off the axis it's much more difficult, maybe even impossible, using "common" functions.