## In This post you will get answer of Q.

Two identical coils of $5$, turns each carry $1, A$ and $2, A$ current respectively. Assume they have common centre with their planes parallel to each other. If their radius is $1 ,m$ 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)

Solution:

## Given, $n=5,, i_{1}=1, A ,, i_{2}=2, A$

We know that, $B=frac{n mu_{0} l a_{1}^{2}}{2left(a^{2}+x^{2}right)^{3 / 2}}$

$B=frac{5 mu_{0} times 2 times 1^{2}}{2(1+3)^{3 / 2}}-frac{5 mu_{0} times 1 times 1^{2}}{2left(1^{2}+3right)^{3 / 2}}$

$B=frac{5 mu_{0} times 2 times 1^{2}}{2^{4}}-frac{5 mu_{0} times 1 times 1^{2}}{2^{4}}$

$B=frac{5 mu_{0}}{16}(2-1), B=frac{5 mu_{0}}{16}(+1)=frac{5 mu_{0}}{16}$