The magnetic field produced at the centre of circular loop of diameter 4 cm is \( 6.28\times10^{-5}\,\mathrm{T} \). The current required to flow in the loop is: \( (\mu_0 = 4\pi\times10^{-7}\,\mathrm{N\,A^{-2}}) \)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2 A
By the Biot-Savart law the field at the centre of a circular loop of radius R carrying a current I is \( B = \mu_0I/2R \). The radius is half the diameter, \( R = 2\,\mathrm{cm} = 0.02\,\mathrm{m} \).
\( \displaystyle I = \frac{2RB}{\mu_0} = \frac{2\times0.02\times6.28\times10^{-5}}{4\pi\times10^{-7}} \)
With \( 6.28 = 2\pi \) the factor \( \pi \) cancels:
\( \displaystyle I = \frac{2\times0.02\times2\times10^{-5}}{4\times10^{-7}} = 2\,\mathrm{A} \)