Question

A current carrying uniform square frame is suspended from hinged supports as shown in the figure such that it can freely rotate about its upper side. The length and mass of each side of the frame are $2$m and $4$kg respectively. A uniform magnetic field $\overline{B}$ = $(3\hat{i}+4\hat{j})$ is applied. When the wire frame is rotated to ${45}^o$ from vertical and released it remains in equilibrium. If the magnitude of current (in A) in the wireframe is $1$ then find $\left(\frac{3}{5}\right)$l.

Answer 1

The length and mass of each side of the frame are $2m$ and $4kg$ respectively.

The uniform magnetic field

$\overrightarrow{B}=(3\hat{i}+4\hat{j})$

Wire frame is roted $=45°$ in

where $n=\frac{l}{2}=\frac{2}{2}=1m$

Current in the wireform $1$

$\left(\frac{3}{5}I\right)$

According to Biotsavart law or Laplace's law

we get,

$\delta B=\frac{9dl\sin \theta }{r^2}$

where

$\delta B=\sqrt{3^2+4^2}=\frac{9\times 2\times \sin 45°}{(1{)}^2}\sqrt{9+16}=\sqrt{25}=5\frac{9\times 2\times \frac{1}{\sqrt{2}}}{1}=5I=\frac{5\sqrt{2}}{2\sqrt{2}}=\frac{5}{\sqrt{2}}=3.535A$