Question

The earth's magnetic field at a given point is $0.5$ $\times 10^{-5} Wb / m ^{2} .$ This field is to be annulled by magnetic induction at the center of a circular conducting loop of radius $5.0\, cm .$ The curtent required to be flown in the loop is nearly

• A. 0.2 A
• B. 0.4 A
• C. 4 A
• D. 40 A

Answer 1

Answer: (B)

The magnetic field at the centre of a circular loop carrying current $I$ is given by $B=\frac{m_{0}I}{2r}$
where $r$ is the radius of the circular loop. Given that
$r = 5.0\, cm = 0.05\, m$.
Now, $B=\frac{\mu_{0}I}{2r}=0.5\times10^{-5}$
$\Rightarrow I=\frac{0.5\times10^{-5}\times2\times0.05}{\mu_{0}}$
$=\frac{0.5\times10^{-5}\times0.1}{4\pi\times10^{-7}}$
$=0.3978\approx0.4\, \mathring{A}$.