Question

Two concentric coils each of radius equal to $2 \pi cm$ are placed at right angles to each other. $3 A$ and $4 A$ 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)

$B_{p}=\frac{\mu_{0} I_{2}}{2 R}$

$=\frac{4 \pi \times 10^{-7} \times 4}{2 \times 0.02 \pi}$
$=4 \times 10^{-5} Wb / m ^{2} $
$ B_{Q} =\frac{\mu_{0} I_{1}}{2 R}$
$=\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} $