Question

Two insulated concentric coils, each of radius R, placed at right angles to each other, carry currents I and `sqrt3 I` respectively. The magnitude of the net magnetic field at their common centre will be ______.

Options

• `(mu_0I)/R`

• `(mu_0I)/(2R)`

• `(mu_0I)/(4R)`

• `(2mu_0I)/R`

Answer 1

Two insulated concentric coils, each of radius R, placed at right angles to each other, carry currents I and `sqrt3 I` respectively. The magnitude of the net magnetic field at their common centre will be `bbunderline((mu_0I)/R)`.

Explanation:

Magnetic field due to circular coil B = `(mu_0I)/(2r)`

`B_1 = (mu_0I)/(2R), B_2 = (mu_0sqrt3I)/(2R)`

Net M.F. |B| = `sqrt(B_1^2 + B_2^2 + 2B_1B_2cos90^circ`    ...[As coils placed at right angle θ = 90°, cos 90° ≈ 0]

`|B| = sqrt(B_1^2 + B_2^2`

= `sqrt(((mu_0I)/(2R))^2 + ((mu_0sqrt3I)/(2R))^2`

= `(mu_0I)/(2R)sqrt(1 + 3)`

= `(mu_0I)/(2R) xx 2`

= `(mu_0I)/R`