Question

Two concentric coils each of radius equal to 2 $\pi$ cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in weber/m${}^2$ at the centre of the coils will be
$({\mu }_0=4\pi \times {10}^{-7}Wb/A.m)$

• A. ${10}^{-5}$
• B. $12\times {10}^{-5}$
• C. $6\times {10}^{-5}$
• D. $7\times {10}^{-5}$

Answer 1

The correct option is D $7\times {10}^{-5}$

The magnetic field due to circular coil,

$B_1=\frac{{\mu }_{0}i}{2r}=\frac{{\mu }_0{i}_1}{2(2\pi \times {10}^{-2})}=\frac{{\mu }_0\times 3\times {10}^2}{4\pi }$

$B_2=\frac{{\mu }_0{i}_2}{2(2\pi \times {10}^{-2})}=\frac{{\mu }_0\times 4\times {10}^2}{4\pi }$

$B=\sqrt{B_1^2+B_2^2}=\frac{{\mu }_0}{4\pi }.5\times {10}^2$

$\Rightarrow B={10}^{-7}\times 5\times {10}^2\Rightarrow B=5\times {10}^{-5}Wb/m^2$