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`         A hollow ,thin-walled insulating cylinder of radius R and length L has charge Q uniformly distributed over its surface.a) caluclate the electric potential at all points along the axis of the tube.Take the orgin to be zero at infinity.b) shoe that  L<`
6 years ago

SAGAR SINGH - IIT DELHI
879 Points
```										Dear student,
V(z) = sigma/(2*epsilon)*(sqrt(R^2 + z^2) - z), where z is the height  above the disc and R is the radius of the disc.  Now try to use this  result to find the potential on the axis of a cylinder length L at a  distance z from its center.
dV = K dQ / r, let dQ = sigma dA, use a geometric argument to get r.   Your dA here is going to have fixed radius (call it R ), so dA = R dz  dphi.  You have angular symmetry, so the integration of d phi is 2 pi.   This combines with K = 1 / (4 pi epsilon).   Your integration of dz will  run from -L/2 to L/2.

All the best.
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Sagar Singh
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```
6 years ago
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