# Electric Field Equation Hollow Cylinder

## Main Question or Discussion Point

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,

## Answers and Replies

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jtbell
Mentor
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.

Meir Achuz
Science Advisor
Homework Helper
Gold Member
More detail please. Is it a conducting cylinder kept at a given potential?
Are the ends open or closed?

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.

Meir Achuz
Science Advisor
Homework Helper
Gold Member
That is impossible. A conducting cylinder will not have a uniform charge.

True that.

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

Meir Achuz
Science Advisor
Homework Helper
Gold Member
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
Mentor
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.