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 ______.

 

Options

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

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

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

• Nothing can be said.

Answer 1

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

Explanation:

To demonstrate this, we will compute the work done by the electric force in an ABCD close loop.

during displacement AD and BC work are done by electric force = 0 as electrostatic is perpendicular to the displacement.

Work done during AB = R ∝ E₁

Work done during CD = -r ∝ E₂

Total work done = R ∝ E₁ - r ∝ E₂

Close loop work done should be zero.

∴ `E_1/E_2 = r/R`