Q. At the centre of a circular coil of radius 5 cm carrying current, magnetic field due to earth is $0.5 \times 10^{- 5}\ {Wbm}^{- 2}.$ What should be the current flowing through the coil so that it annuals the earth’s magnetic field?
A) 40 A
B) 4 A
C) 0.4 A
D) 0.2 A
Explanation
(c) Magnetic field $(B)$ at the centre of a coil of radius $(r)$ carrying current $(i)$ is
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B = \frac{\mu_{0}i}{2r}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ i = \frac{2rB}{\mu_{0}}$
Given, $B = 0.5 \times 10^{- 5}\ T,\ r = 0.05\ m$
$\ i = \frac{2 \times 0.5 \times 10^{- 5} \times 0.05}{4\pi \times 10^{- 7}} = 0.398\ A$
$\Rightarrow i \approx 0.4\ A$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.