Question

A wire carrying current $I$, bent in the form of a quarter circle, is held at rest on a smooth table with two threads as shown. A uniform magnetic field exists in the region directed into the plane, select the correct alternatives.

• A. Net force on wire is zero
• B. Net magnetic force on wire is $BIR\sqrt{2}$
• C. Tension in the threads is $BIR$
• D. Tension in the threads is $BIR\sqrt{2}$

Answer 1

Answer: (A), (B), (C)

Tension in the threads is $BIR$

FBD:


From the $FBD$ of quarter circle wire, magnetic force on it
${\overrightarrow{F}}_B=I\overrightarrow{l}\times \overrightarrow{B}$

$\Rightarrow |{\overrightarrow{F}}_B|=IlB\sin {90}^{\circ }$

Here, $l=$effective length so,$l=\sqrt{R^2+R^2}=R\sqrt{2}$

$\Rightarrow F_B=\sqrt{2}RIB$

Since, the wire is held at rest, so the net force on the wire must be zero.

$\therefore F_1=T=F_B\cos {45}^{\circ }$

$\Rightarrow T=\frac{F_B}{\sqrt{2}}$

$\therefore T=\frac{\sqrt{2}RIB}{\sqrt{2}}=RIB$

Hence, options (a) , (b) and (c) are the correct answers.