Question

Two coils $'P'$ and $'Q'$ are separated by some distance. When a current of $3\, A$ flows through coil $'P'$, a magnetic flux of $10^{-3}\, Wb$ passes through $'Q'$. No current is passed through $'Q'$. When no current passes through $'P'$ and a current of $2\, A$ passes through $'Q'$, the flux through $'P'$ is :

• A. $ 6.67 \times 10^{-3} \; Wb$
• B. $ 6.67 \times 10^{-4} \; Wb$
• C. $ 3.67 \times 10^{-4} \; Wb$
• D. $ 3.67 \times 10^{-3} \; Wb$

Answer 1

Answer: (B)

$\phi_{q} = \frac{\mu_{0} i_{1}R^{2}}{2\left(R^{2} +x^{2}\right)^{\frac{3}{2}}} \times\pi r^{2} = 10^{-3} $
$ \phi_{p} = \frac{\mu_{0}i_{2}r^{2}}{2\left(r^{2}+x^{2}\right)^{\frac{3}{2}}} \times\pi R^{2}$
$ \frac{\phi_{P}}{\phi_{Q} } = \frac{i_{2}}{i_{1}} . \frac{\left(R^{2} +x^{2}\right)^{\frac{3}{2}}}{\left(r^{2} +x^{2}\right)^{\frac{3}{2}}} = \frac{\phi_{P}}{10^{-3}} $
$ \frac{2}{3} = \frac{\phi_{P}}{10^{-3}} $
$ \phi_{P} = 6.67 \times10^{-4} $