Question

A point P lies on the axis of a flat coil carrying a current. The magnetic moment of the coil is $\pi$. The distance of P from the coil is d, which is large compared to the radius of the coil. The magnetic field at P has magnitude

• A. $\frac{{\mu }_0}{2\pi }\left[\frac{\pi }{d^3}\right]$
• B. $\frac{{\mu }_0}{4\pi }\left[\frac{\pi }{d^3}\right]$
• C. $\frac{{\mu }_0}{6\pi }\left[\frac{\pi }{d^2}\right]$
• D. $\frac{{\mu }_0}{8\pi }\left[\frac{\pi }{d^2}\right]$

Answer 1

The correct option is A $\frac{{\mu }_0}{2\pi }\left[\frac{\pi }{d^3}\right]$

The magnetic field at P due to the flat coil of n turns, radius r, carrying current i is
$B=\frac{{\mu }_0}{2}.\frac{ni{r}^2}{(d^2+r^2)}\cong \frac{{\mu }_0}{2}.\frac{ni{r}^2}{d^3}(d>>r)=\frac{{\mu }_0}{2\pi },\frac{n\left(\pi r^2\right)}{d^3}=\frac{{\mu }_0}{2\pi }.\frac{\pi }{d^3}.$