Question

There is a circular disc with charge density Sigma uniformly distributed over it. The disc has a radius a. A hole of radius b (b<a) is cut into the disc. Find V along the central axle. Use dV = -E Vector .d S Vector to find E Vector.

Answer 1

Charge on the ring is given by dQ = sigma dA = sigma 2 pi r d r = 8 Q/3R^2 rdr Expression for the potential is given by dv = 2/3 pi e_0 Q/R^2 rdr/squareroot z^2 + r^2 The total electric potential due to the annulus is given by V = 2/3piE_0 Q/R^2intergal_b^a rdr/squareroot z^2 + r^2 V = 2/3pi e_0 Q/R^2(squareroot z^2 + a^2 - squareroot z^2 + b^2)