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

0.4 A

The correct answer is Option (3) → 0.4 A

Magnetic field at the center of a circular loop is

$B = \frac{\mu_0 I}{2R}$

Here, $B = 0.5 \times 10^{-5} \, Wb/m^2$, $R = 0.05 \, m$, $\mu_0 = 4\pi \times 10^{-7} \, Tm/A$

So, $I = \frac{2RB}{\mu_0}$

$I = \frac{2 \times 0.05 \times 0.5 \times 10^{-5}}{4\pi \times 10^{-7}}$

$I = \frac{5 \times 10^{-7}}{4\pi \times 10^{-7}}$

$I = \frac{5}{4\pi} \approx 0.4 \, A$

Final Answer: 0.4 A