Question

If the electric lines of force are shaped like arcs of concentric circles with their centre at point $O$ in a certain section of an electric field, then

• A. The intensity of the field in this section should at each point be inversely proportional to its distance from point O
• B. The intensity of the field in this section should at each point be inversely proportional to square of its distance from point O
• C. The intensity of the field in this section should at each point be inversely proportional to cube of its distance from point O
• D. Nothing can be said

Answer 1

Answer: (A)

To prove this we will calculate work done by electric force in a close loop ABCD.


During displacement AD and BC work done by electric force = 0 as electrostatic is perpendicular to displacement.
Work done during $AB=R \, \alpha \, E_{1}$
Work done during $CD=-r \, \alpha \, E_{2}$
Total work done $=R \, \alpha \, E_{1}-r \, \alpha \, E_{2}$
Close loop work done should be zero
$\therefore \frac{E_{1}}{E_{2}}=\frac{r}{R}$