Question

Pick out the expression for magnetic field strength at any point at the center of a circular loop from the following?

(a) B = \( [ \frac {\mu_o I}{4 \pi r} ] \int_0^{2\pi r} \)dl  sin⁡90

(b) B = \( [ \frac {\mu_o I}{4 \pi r} ] \int_0^{2\pi r} \)dl sin⁡45

(c) B = \( [ \frac {\mu_o I}{4 \pi r} ] \int_0^{2\pi r} \)dl sin⁡30

(d) B = [μo ×  4πr]\( \int_0^{2\pi r} \)dl  sin⁡90

This question was addressed to me during an interview.

My question is taken from Magnetic Field on the Axis of a Circular Current Loop in division Moving Charges and Magnetism of Physics – Class 12

Answer 1

The correct option is (a) B = \( [ \frac {\mu_o I}{4 \pi r} ] \int_0^{2\pi r} \)dl  sin⁡90

Best explanation: The magnetic field strength at any point at center of circular loop carrying current I and radius r is given as:

B = \( [ \frac {\mu_o I}{4 \pi r} ] \int_0^{2\pi r} \)dl  sin⁡90

It can also be expressed as → B = \( [ \frac {\mu_o I}{4 \pi r} ] \) × 2πr  or B = \( [ \frac {\mu_o I}{2 r} ] \) direction.

It is inwards if the current is flowing in the clockwise direction and it is onwards if the current is flowing in the anticlockwise direction.