Question

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

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

Answer 1

Answer: (C)

$5\times {10}^{-5}$

Magnetic induction due to coil $1=\overrightarrow{B_1}=\frac{{\mu }_{0}I}{2R}=\frac{40\times {10}^{-7}\times 3}{2\times 2\varphi \times {10}^{-2}}=3\times {10}^{-5}$

Magnetic induction due to coil $2=\overrightarrow{B_2}=\frac{{\mu }_{0}I}{2R}=\frac{4\varphi \times {10}^{-7}\times 4}{2\times 2\varphi \times {10}^{-2}}=4\times {10}^{-5}$

$\overrightarrow{B_1}$ and $\overrightarrow{B_2}$will be perpendicular to each other

$B_{net}=\sqrt{B_1^2+B_2^2}=5\times {10}^{-5}$