A magnetic field of \( 0.5\times10^{-5}\,\mathrm{T} \) at a point is to be cancelled by the magnetic field at the centre of a circular conducting loop of radius 5.0 cm placed there. The current required in the loop is nearly
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.4 A
The magnetic field at the centre of a circular loop of radius R carrying current I is \( B=\mu_0I/2R \), directed along the axis of the loop. The loop must be placed so that its field at the centre is equal in magnitude and opposite in direction to the given field.
In SI units, with \( \mu_0=4\pi\times10^{-7}\,\mathrm{T\,m\,A^{-1}} \):
\( B=0.5\times10^{-5}\,\mathrm{T} \)
\( R=5.0\,\mathrm{cm}=0.05\,\mathrm{m} \)
Equating the field of the loop to the given field:
\( \displaystyle \frac{\mu_0I}{2R}=B \)
\( \begin{aligned} I &= \frac{2RB}{\mu_0} \\ &= \frac{2\times0.05\,\mathrm{m}\times0.5\times10^{-5}\,\mathrm{T}}{4\pi\times10^{-7}\,\mathrm{T\,m\,A^{-1}}} \\ &\approx 0.40\,\mathrm{A} \end{aligned} \)