Question

A square wire frame of linear mass density $\lambda =3kg/m$ and side length, $3m$ carrying a current of $4A$ with its plane in X –Y plane. A uniform magnetic field $B=2T$ is directed along y –axis. The initial angular acceleration of the frame in $rad/s^2$ is
[Answer upto two decimal points]

Answer 1

$i=4A$, $L=3m$, $M=i{L}^2$
$\tau =MB\Rightarrow I\alpha =i{L}^{2}B;....\left(1\right)$
where $I$ is the moment of inertia of the frame about its centre.
$I=2\left[\frac{\lambda L}{12}{L}^2\right]+2\left(\lambda L\right){\left(\frac{L}{2}\right)}^2=\frac{2\lambda L^3}{3}....\left(2\right).$ From (1) and (2) $\alpha =\frac{3Bi}{2\lambda L}=\frac{4}{3}rad/s^2$