Question

The magnetic field at the centre of a loop of a circular wire of radius $r$ carrying current $I$ may be taken as $B_{0}$. If a particle of charge $q$ moving with speed $v$ passes the centre of a semicircular wire, as shown in figure, along the axis of the wire, the force on it due to the current is :

• A. zero
• B. $\frac{1}{4} B_{0} q v$
• C. $\frac{1}{2} q B_{0} v$
• D. $q B_{0} v$

Answer 1

Answer: (C)

Magnetic field induction at $P=0$, magnetic field induction at $O=B_{0}$. Average magnetic field induction from $P$ to $O=\frac{0+B_{0}}{2}=\frac{B_{0}}{2}$
Force experienced by a charge while moving along the axis of wire, i.e., from $P$ to $O$ will be
$=\frac{B_{0}}{2} \times q \times v $
$=\frac{1}{2} B_{0} \,q v$