Question

A wheel with 4 spokes is placed with its plane perpendicular to a uniform magnetic field B of magnitude 0.5 T. The field is directed into the plane of the paper and is present over the entire region of the wheel as shown in fig. When the switch S is closed, there is initial current of 6 A between the axis and the rim and the wheel begins to rotate. Resistances of the spokes are 1, 2, 4 and $8\Omega$, respectively. Resistance of rim is negligible.
If current in $1\Omega$ is 2/X A. Find X?

Answer 1

$B=0.5T;i=6A$$i_1:i_2:i_4:i_8::1:\frac{1}{2}:\frac{1}{4}:\frac{1}{8}$
$\therefore x+\frac{1}{2}x+\frac{1}{4}x+\frac{1}{8}x=6$
$\Rightarrow x\frac{15}{8}=6\Rightarrow x=\frac{16}{5}$
$\therefore i_1=\frac{16}{5}A,i_2=\frac{8}{5}A,i_4=\frac{4}{5}A,i_8=\frac{2}{5}A$
The forces acting on spokes are as shown in fig. Hence, the wheel starts rotating in the anticlockwise direction.