Question

When equal current is passed through two coils equal magnetic field is produced at their centres in the ratio of number of turns in the coil is 8:15 in the ratio of their radii will be?

Answer 1

Explanation:

The magnetic field at the center of the a coil is given by :

$B=\dfrac{\mu_oI}{2r}$

For n number of turns,

$B=\dfrac{\mu_oIn}{2r}$

Given that, $\dfrac{n_1}{n_2}=\dfrac{8}{15}$

Since, B and I for both coils are same. So,

For coil 1, $B=\dfrac{\mu_oIn_1}{2r_1}$

For coil 2, $B=\dfrac{\mu_oIn_2}{2r_2}$

Taking ratios of above equations :

$\dfrac{n_1}{n_2}=\dfrac{r_1}{r_2}$

So, $\dfrac{r_1}{r_2}=\dfrac{8}{15}$

Hence, this is the required solution.