Question

A toroid of narrow radius of 10 cm has 1000 turns of wire. For a magnetic field of 5 × 10^-2 T along its axis, how much current is required to be passed through the wire?

Answer 1

Data : CentraI radius, r = 10 cm = 0.1 m, N = 1000,
B = 5 × 10^-2 T, = 4π × 10^-7 T∙m/A
The magnetic induction,
B = $\frac{{\mu }_{0}NI}{2\pi r}=\frac{{\mu }_0}{4\pi }\frac{2NI}{r}$
2irr 4ir r
∴ 5 × 10^-2 = 10^-7 × $\frac{2(1000)I}{0.1}$
∴ I = $\frac{50}{2}$ = 25A
This is the required current.