Topic: Electromagnetics
The force on a point charge +q kept at a distance d from the surface of an infinite grounded metal plate in a medium of permittivity $\epsilon$ is
- A. 0
- B. $\frac{q^{2}}{16\pi\epsilon d^{2}}$ away from the plate
- C. $\frac{q^{2}}{16\pi\epsilon d^{2}}$ towards the plate
- D. $\frac{q^{2}}{4\pi\epsilon d^{2}}$ towards the plate
Answer: C. $\frac{q^{2}}{16\pi\epsilon d^{2}}$ towards the plate
Explanation: By the method of images, the grounded plate is replaced by an image charge $-q$ at a distance $d$ behind the plate. The distance between the original charge and the image charge is $2d$. The force is $F = \frac{q \times (-q)}{4\pi\epsilon(2d)^2} = -\frac{q²}{16\pi\epsilon d²}$. The negative sign indicates an attractive force towards the plate.