Question

The wire loop PQRS formed by joining two semi circular wire of radii $R_1$ and $R_2$ carries a current I as shown. The magnitude of magnetic induction at the centre O is

• A. $\left({\mu }_0/4\right)I(R_1/R_2-1/R_1)$
• B. $\left({\mu }_0/4\right)I(1/R_1-1/R_2)$
• C. ${\mu }_{0}I(1/R_1-1/R_1)$
• D. ${\mu }_{0}I\left(1/R_1\right)$

Answer 1

The correct option is B $\left({\mu }_0/4\right)I(1/R_1-1/R_2)$

Magnetic field field due to a semi circular arc of radius $r$ at the center of the circle=$\frac{{\mu }_{0}I}{2r}$

Hence magnetic field upwards due to inner semicircle=$\frac{{\mu }_{0}I}{4R_1}$

and magnetic field upwards due to outer semicircle=$\frac{{\mu }_{0}I}{4R_2}$

Hence net magnetic field at the center of the semicircle upwards=$\frac{{\mu }_{0}I}{4}(\frac{1}{R_1}-\frac{1}{R_2})$