Question

If the magnetic lines of force are shaped like arcs of concentric circles with their centre at point O in a certain section of a magnetic field:

• 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)

The intensity of the field in this section should at each point be inversely proportional to its distance from point O

Answer 2

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 α E₁

Work done during CD = – r α E₂

Total work done = R α E₁ – r α  Ε₂

Close loop work done should be zero

∴ $\frac { E _ { 1 } } { E _ { 2 } } = \frac { r } { R }$