Question

Two identical coils of $5$ turns each carry $1A$ and $2A$ current respectively. Assume that they have common centre with their planes parallel to each other. If their radius is $1m$ each and the direction of flow of current in the coils are in opposite directions, then the magnetic field produced on its axial line at a distance of $\sqrt{3}m$, from the common centre is (in tesla).

• A. $0$
• B. $\frac{15}{16}{\mu }_0$
• C. $\frac{8}{16}{\mu }_0$
• D. $\frac{5}{16}{\mu }_0$
• E. $\frac{16}{5}{\mu }_0$

Answer 1

Answer: (D)

$\frac{5}{16}{\mu }_0$

Given, $n=5,i_1=1A,i_2=2A$
We know that, $B=\frac{n{\mu }_{0}i{a}_1^2}{2(a^2+x^2{)}^{3/2}}$
$B=\frac{5{\mu }_0\times 2\times 1^2}{2(1+3{)}^{3/2}}-\frac{5{\mu }_0\times 1\times 1^2}{2(1^2+3{)}^{3/2}}$
$B=\frac{5{\mu }_0\times 2\times 1^2}{2^4}-\frac{5{\mu }_0\times 1\times 1^2}{2^4}$
$B=\frac{5{\mu }_0}{16}(2-1),B=\frac{5{\mu }_0}{16}(+1)=\frac{5{\mu }_0}{16}$.