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. $7\times {10}^{-5}$
• D. $5\times {10}^{-5}$

Answer 1

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

$B_1=\frac{m{u}_0{i}_1}{2\left(2\pi \right)}=\frac{{\mu }_0\times 3}{4\pi }$

$B_2=\frac{m{u}_0{i}_2}{2\left(2\pi \right)}=\frac{m{u}_0\times 4}{4\pi }$

$B=\sqrt{B_1^2+B_2^2}=\frac{m{u}_0}{4\pi }\cdot 5$

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

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