Question

A circular arc of radius 'r' carrying current 'I' subtends on angle `pi/16` at its centre. The radius of a metal wire is uniform. The magnetic induction at the centre of circular arc is ____________.

Options

• `(mu_0 "I")/(64 "r")`

• `(mu_0 "I")/(8 "r")`

• `(mu_0 "I")/(32 "r")`

• `(mu_0 "I")/(16 "r")`

Answer 1

A circular arc of radius 'r' carrying current 'I' subtends on angle `pi/16` at its centre. The radius of a metal wire is uniform. The magnetic induction at the centre of circular arc is `(mu_0 "I")/(64 "r")`.

Explanation:

`varphi = "r" xx pi/16`

Magnetic field at the centre of the loop due to entire circular loop is

`"B" = (mu_0 "I")/(2"r")`

`therefore "Magnetic field due to"  varphi  "is"`

`"B"_varphi = (mu_0 "I")/(2"r") xx 1/(2pi"r") xx (pi"r")/16 = (mu_0 "I")/(64 "r")`