Question

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

${\varphi }_q=\frac{{\mu }_0{i}_1{R}^2}{2{\left(R^2+x^2\right)}^{\frac{3}{2}}}\times \pi r^2=10^{-3}$
${\varphi }_p=\frac{{\mu }_0{i}_2{r}^2}{2{\left(r^2+x^2\right)}^{\frac{3}{2}}}\times \pi R^2$
$\frac{{\varphi }_P}{{\varphi }_Q}=\frac{i_2}{i_1}.\frac{{\left(R^2+x^2\right)}^{\frac{3}{2}}}{{\left(r^2+x^2\right)}^{\frac{3}{2}}}=\frac{{\varphi }_P}{10^{-3}}$
$\frac{2}{3}=\frac{{\varphi }_P}{10^{-3}}$
${\varphi }_P=6.67\times 10^{-4}$