Question

For case 1) above (single coil), write an expression relating the slope of a B vs I plot in terms to μ0, N, and R. You will use this expression to calculate the value of the constant μ0 later on.

Answer 1

Since you have not given the name of specific coil or any diagram I am assuming it to be the toroid coil of mean radius R.

For a toroid coil the magnetic field at a mean distance R is given as

$\oint Bdl = \mu_0 N I$

$B\oint dl = \mu_0 N I$

$B(2\pi R)= \mu_0 N I$

$B= \frac{\mu_0 NI}{2\pi R}$

So the slope of the curve between B vs I

slope = $\frac{\mu_0 N}{2\pi R}$