Question

Two concentric coils each of radius equal to $2\pi cm$ 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 $\left({\mu }_0=4\pi \times 10^{-7}Wb/Am\right)$

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

Answer 1

Answer: (C)

$B_p=\frac{{\mu }_0{I}_2}{2R}$

$=\frac{4\pi \times 10^{-7}\times 4}{2\times 0.02\pi }$
$=4\times 10^{-5}Wb/m^2$
$B_Q=\frac{{\mu }_0{I}_1}{2R}$
$=\frac{4\pi \times 10^{-7}\times 3}{2\times 0.02\pi }=3\times 10^{-5}Wb/m^2$
$\therefore B=\sqrt{B_P^2+B_Q^2}$
$=\sqrt{{\left(4\times 10^{-5}\right)}^2+{\left(3\times 10^{-5}\right)}^2}$
$=5\times 10^{-5}Wb/m^2$