Question

The wire loop PQRSP formed by joining two semicircular wires of radii $R_{1}and{R}_2$ carries a current 7 as shown. The magnitude of the magnetic induction at the centre C i s .......

Answer 1

At C magnetic field due to wires PQ and RS will be zero. Due
to wire QR
$B_1=\frac{1}{2}\left(\frac{{\mu }_{0}I}{2R_1}\right)=\frac{{\mu }_{0}I}{4R_1}$ (perpendicular to paper outwards)
And due to wire SP
$B_2=\frac{1}{2}\left(\frac{{\mu }_{0}I}{2R_2}\right)=\frac{{\mu }_{0}I}{4R_2}$ (perpendicular to paper inwards)
$\therefore$ Net magnetic field would be,
$B=\frac{{\mu }_{0}I}{4}(\frac{1}{R_1}-\frac{1}{R_2})$ (perpendicular to paper outwards)