Question

A conducting wire bent in the shape of a parabola $y^2=2x$ carries a current of $2\text{A}$ as shown. This wire is placed in a uniform magnetic field $\overrightarrow{B}=-4\hat{k}$. The magnitude of force on the wire is (Give integer value)

Answer 1

The magnitude of force will be

$F_m=BI{l}_{AB}$

Where, $l_{AB}$ is effective length between the points $A$ and $B$.

Now, $\text{x-}$coordinate of both $A$ and $B$ will be equal.

Given equation of parabola is
$y^2=2x$

At, $x=2$ ,

$\Rightarrow y^2=2\times 2=4$ $\Rightarrow y=\pm 2$

$\therefore A=(2,2)$ and $B=(+2,-2)$

$\therefore l_{AB}=4\text{m}$

$\Rightarrow F_m=4\times 2\times 4=32\text{N}$

Accepted answer: $32$