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. $\frac{1}{4}{B}_{0}qv$
• 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
$=\frac{B_0}{2}\times q\times v$
$=\frac{1}{2}{B}_{0}qv$