Question

2. A uniformly charged disk with a diameter of 30 cmn has a total charge of 10 uC. Find the electric field on the axis of the disk at 2 cm (a), 6 cm (b), 45 cm (c), and 5 m (d) from the center of the disk.

Would someone please explain how to work this out with steps? Thanks in advance!

Answer 1

The electric field of uniformly charged disk assuming the plane of the disk is in x-y plane and the axis passing through the centre is along positive zaxis E_z = sigma/2 epsilon_0[1 - z/squareroot z^2 + R^2] z is the distance of the point from the centre of the disk k_e = coloumb constant = 8.98 times 10^9 N.m^2 C^- 2 R = radius of the conducting disk = 15cm sigma = Q/A = Q/pi R^2 = 141.5 mu c/m^2 given at appoint z on the positive zaxis, E_z = sigma/2 epsilon_0(1 - z/squareroot z^2 + R^2] sigma/2 epsilon_0 = 7.989e + 06 when z = 2.0cm we plug the values in hand while using the relation give us implies E_z = sigma/2 epsilon_0(1 - z/squareroot z^2 + R^2) = 6.933e + 06 N/C implies when z = 6.0 cm implies E_z = sigma/2 epsilon_0(1 - s/squareroot z^2 + R^2) = 5.022e + 006 N/C implies when z = 45.0cm implies E_z = sigma/2 epsilon_0