Question

There is a grounded conducting plane on the xy plane and a grounded hemisphere of radius R, in the positive z-axis, centered at the origin. We put a point charge +Q on the z-axis, and its distance from the origin is S. Find the force on the point charge.

Answer 1

So, we placed a charge + Q on the z axis, infront of a grounded hemisphere & a conducting plane. So: Due to the hemisphere we will have an image charge q^1 = -RQ/S at a position d^1 = R^2/S, from origin. Now, this charge q^1 will have its own image charge, as it is infront of the conducting plane. So, Due to the conducting plane + Q will form an image charge -Q at z = -5 & q^1 will form an image charge at z = -d^1 = -R^2/S position. So, Force on the charge + Q. (1) force due to q^1 at R^2/S = 1/4pi epsilon_0 q^1Q/(s-d^1) ^2 hat z = 1/(4pi epsilon_0) Q.(-) RQ/s/(s-R^2/s) ^2 hat z = -1/4pi epsilon_0 RQ^2/s/(s-R^2/s) ^2 hat z F_q^1 = -1/4pi epsilon_0 RQ^2/s[s^2-R^2/sy]^2 hat z Rightarrow F_q^1 = -1/4pi epsilon_0 RQ^2S/(s^2-R^2) ^2 hat z (2) Force due