Question

A wire in shape of thin cylindrical shell carries current i as shown in figure.

• A. If current is switched off, crossection area of wire increases.
• B. Force exerted by half wire on the other half per unit length is $\frac{{\mu }_0{I}^2}{4{\pi }^{2}R}$.
• C. Force exerted by half wire on other half per unit length is $\frac{{\mu }_0{I}^2}{16{\pi }^{2}R}$.
• D. Magnetic field inside the wire is zero.

Answer 1

Answer: (A), (B), (D)

Magnetic field inside the wire is zero.

When current is flowing through the wire, the first half will attract the other half. When the current is switched off the wire will expand and cross-sectional area of wire will increase.

Let's consider a small element which subtends an angle $d\theta$ as shown in figure.
Let the force on that element per unit length be $dF$.
It is observed that we are left with only the horizontal component.
So, $dF=\frac{{\mu }_0{I}^{2}sin\theta d\theta }{4\pi R\times 2\pi }$

After integrating from 0 to $\pi$ the force exerted on one half by the other half comes out to be $\frac{{\mu }_0{I}^2}{4{\pi }^{2}R}$ .

As it is a conducting hollow cyllinder, magnetic field inside the wire is zero.