Question

What will be the value of the magnetic field at the centre in the given figure? The coil is made of a uniform wire and is connected with two long straight wires. Assumes r is the radius of coil.

• A. $\frac{{\mu }_0}{4\pi }\left[\frac{i}{r}\right]$
• B. $\frac{{\mu }_0}{4\pi }\left[\frac{2\pi i}{r}\right]$
• C. $\frac{{\mu }_0}{4\pi }[\frac{2i}{r}+\frac{2\pi i}{r}]$
• D. $0$

Answer 1

Answer: (B)

$\frac{{\mu }_0}{4\pi }\left[\frac{2\pi i}{r}\right]$

Here magnetic field at the centre is only due to the circular coil. The magnetic field due to two long straight wire will be zero each as the centre of the circle coincide with the length of the two straight conductors if extended. Thus magnetic field is given by

$B=\frac{{\mu }_0}{4\pi }\left(\frac{2\pi i}{r}\right)$