Answer to Question #92196 in Mechanics | Relativity for Sridhar

Question

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at P, in the region, is found to vary between the limits 589.0V to 589.8V. What is the potential at a point on the sphere whose radius vector makes an angle of 600 with the direction of the field ?
(1)589.5V(2)589.2V(3)589.4V(4)589.6V

Answer 1

Potential gradient is equal to

$$v=589.8 V – 589.0 V = 0.8 V (1)$$

Potential gradient is given by formula:

$$v=Ed \cos 60° (2)$$

Using (1) and (2) we got:

$$v=0.8 V×0.5 =0.4 V (3)$$

The potential at a point on the sphere is equal to

$$v=589.0 + 0.4 V= 589.4 V$$

Answer:

(3)589.4V