Question

Figure shows a wire of arbitrary shape of carrying $a$ current $i$ between points $a$ and $b$ . Let the length of the wire be $L$ and the distance between points $a$ and $b$ be $d$ . The wire lies in a plane at right angle to a uniform magnetic field $B$ . Then what is the force on the wire ?

• A. iLB
• B. idB
• C. $i\left(L-d\right)B$
• D. none of the above

Answer 1

Answer: (A)

The force on a current carrying conductor in a uniform magnetic field is given by
$F=ilBSin\theta$
Here we have to consider only the effective length of the wire, which is equal to $d$ .
$l=d\theta =90^{\circ }\Rightarrow sin90^{\circ }=1$
So, the force on the wire will be equal to $idB$