Question

Inside a long straight uniform wire of circular cross - section there is a long cylindrical cavity of radius $r$ whose axis is parallel to the axis of the wire. Axis of cavity is displaced from the axis of wire by a distance $L$ as shown in figure. A direct current density $J$ flows through the wire. Then

(I) Magnetic field inside the cavity is non-uniform

(II) Magnetic field inside the cavity is uniform

(III) Field inside the cavity is directly proportional to $L$

(IV) Magnetic field inside the cavity is independent of $L$

• A. I and IV
• B. I and III
• C. II and IV
• D. II and III

Answer 1

The correct option is D

II and III

By superposition theorem Magnetic Field inside the cavity in a long straight wire is given by
$\overrightarrow{B}=\frac{{\mu }_0}{2}(\overrightarrow{J}\times \overrightarrow{L})$
So Magnetic field inside the cavity is uniform and proportional to $L$