The earth's magnetic field at a given point is \( 0.5\times10^{-5}\,\mathrm{Wb/m^2} \). 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
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 0.4\,\mathrm{A} \)
To annul the earth's field, the field at the centre of the loop must be equal to it in size and opposite in direction. By the Biot-Savart law the field at the centre of a circular loop is
\( \displaystyle B = \frac{\mu_0 I}{2R} \)
\( R = 5\,\mathrm{cm} = 5\times10^{-2}\,\mathrm{m} \)
\( B = 0.5\times10^{-5}\,\mathrm{T} \)
\( \displaystyle I = \frac{2RB}{\mu_0} = \frac{2 \times 5\times10^{-2} \times 0.5\times10^{-5}}{4\pi\times10^{-7}} = \frac{5\times10^{-7}}{4\pi\times10^{-7}} = \frac{5}{4\pi} \approx 0.4\,\mathrm{A} \)