Question

A circular arc of radius 'r' carrying current 'I subtends an angle `(pi/32)^c` at its centre. The radius 32 of a metal wire is uniform. The magnetic induction at the centre of the circular arc is ______. (μ₀ = permeability of vacuum) (sin 90° = 1)

Options

• `(mu_0I)/(16 r)`

• `(mu_0I)/(32 r)`

• `(mu_0I)/(64 r)`

• `(mu_0I)/(128 r)`

Answer 1

A circular arc of radius 'r' carrying current 'I subtends an angle `(pi/32)^c` at its centre. The radius 32 of a metal wire is uniform. The magnetic induction at the centre of the circular arc is `bbunderline((mu_0I)/(128 r))`. (μ₀ = permeability of vacuum) (sin 90° = 1)

Explanation:

The magnetic induction (B) at the centre of a circular arc of radius r, carrying a current I, and subtending an angle θ (in radians) at the center is given by the formula:

B = `(mu_0 I)/(4pir) xx theta`

∴ B = `(mu_0 I)/(4pir) xx (pi/32)`

∴ B = `(mu_0 I)/(128 r)`