Question

When an arc of a circle of radius R subtends an angle of \(\frac {\pi }{4}\)  at the center, and carries a current I, the magnetic field at the center is B = \(\frac {\mu_o I}{16R}\).

(a) True

(b) False

The question was posed to me in an interview for job.

I would like to ask this question from Magnetic Field on the Axis of a Circular Current Loop topic in section Moving Charges and Magnetism of Physics – Class 12

Answer 1

The correct option is (a) True

For explanation: Magnetic field at the center of a circular arc of radius R, carries a current I and makes an angle θ at the center is given by

B = \(\frac {\mu_o I \theta}{4 \pi R}\)

In this case θ = \(\frac {\pi }{4}\)

B = \(\frac {\mu_o I (\frac {\pi }{4})}{4 \pi R}\)

B = \(\frac {\mu_o I}{16 R}\)