Question

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii \(R_1 = 2\pi\, m\) and \(R_2 = 4\pi \,m\) carrying current I = 4A as per figure given below is \(\alpha \times 10^{-7}\, T\) . The value of \(\alpha\) is ______. (Centre O is common for all segments)

Answer 1

The value of \(\alpha\) is 3.

\(\cfrac{\mu_0i}{2R_2}(\cfrac{\pi}{2\pi}) \otimes + \cfrac{\mu_0i}{2R_1}(\cfrac{\pi}{2\pi}) \otimes\)

\((\cfrac{\mu_0i}{4R_2} + \cfrac{\mu_0i}{4R_1})\otimes\)

\(\frac{4\pi \times 10^{-7} \times 4}{4 \times 4\pi} + \frac{4\pi \times 10^{-7} \times 4}{4 \times 2\pi}\)

\(3 \times 10^{-7} = α \times 10^{-7}\)

\(α = 3\)