Question

A current carrying solenoid produces a magnetic field around it. The distance of a point $A$, situated on the perpendicular bisector of the length of the solenoid, is $R$ from its center. Another point $P$ is situated on its axis, at a distance $4R$ from its center. Find the ratio of magnetic field at point $P$ to the magnetic field at point $A$.

• A. $1:4$
• B. $1:16$
• C. $1:32$
• D. $1:64$

Answer 1

The correct option is C $1:32$

The magnitude of magnetic field due to a solenoid, acting as a bar magnet, at a point (outside) on its axis is given by,

$\therefore B_P=\frac{{\mu }_0}{4\pi }\frac{2M}{r^3}$

$\Rightarrow B_P=\frac{{\mu }_0}{4\pi }\frac{2M}{(4R{)}^3}=\frac{{\mu }_0}{4\pi }\frac{M}{32R^3}$

The magnitude of magnetic field due to a solenoid, acting as a bar magnet, at a point (outside) on its equator is given by,

$\therefore B_A=\frac{{\mu }_0}{4\pi }\frac{M}{r^3}$

$\Rightarrow B_A=\frac{{\mu }_0}{4\pi }\frac{M}{R^3}$

Now,

$\frac{B_P}{B_A}=\frac{\frac{{\mu }_0}{4\pi }\frac{M}{32R^3}}{\frac{{\mu }_0}{4\pi }\frac{M}{R^3}}=\frac{1}{32}=1:32$

Hence, option $\left(C\right)$ is the correct answer.