question_answer

The magnetic field at the centre of a loop of a circular wire of radius r carrying current I may be taken as B0. If a panicle 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)  \[\frac{1}{4}\]B0 qv

C)  \[\frac{1}{2}q{{B}_{0}}v\]

D)  \[q{{B}_{0}}v\]

Correct Answer: C

Solution :

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 alotig the asds of wire, l?-, from P to O will be \[=\frac{{{B}_{0}}}{2}\times q\times v\] \[=\frac{1}{2}{{B}_{0}}qv\]