Answer to Question #155741 in Physics for qudsia

Question

Question-3

In Fig. 3, 12 electrons (of charge e) are equally spaced and fixed around a circle of radius R. Relative to V=0 at infinity, what are the electric potential and electric field at the center C of the circle due to these electrons?

Fig-3 (a) twelve electrons uniformly spaced around a circle. (b)The electrons no uniformly spaced along an arc of the original circle.

Answer 1

we have 12 electrons uniformly spaced along a circle and each creates a field

$$E=\frac{ke}{R^2}.$$

Each electron creates a field that is directed toward an electron, so, since we have even number of electrons, the field of every two electrons is canceled and the resultant field is 0.

The electric potential is a scalar additive quantity, so, the potential from a single electron is

$$\phi=\frac{ke}{Rr}.$$

12 electrons create

$$\Phi=\frac{12ke}{R}.$$