Question

A coil wrapped around a toroid has inner radius of \( 20.0 cm \) and an outer radius of \( 25.0 cm \). If wrapping makes 800 turns and carries a current of \( 12.0 A \), what are the maximum and minimum of the magnetic field within the toroid?

Answer 1

Magnetic field inside the toroid B = \(\mu_0Ni\)

\(\because n = \frac{no.\, of\, turns}{length}\)

\(B = \frac{\mu_0 Ni}l\)

\(l = 2\pi r\)

\(B= \frac{\mu_0Ni}{2\pi r}\)

r₁ = 20 cm = 0.2 m

r₂ = 25 cm = 0.25 m

i = 12 A, N = 800

\(B_{max} = \frac{\mu_0Ni}{2\pi r_1}\)

\(= \frac{2 \times 10^{-7}\times800\times12}{0.20}\)

\(B_{max} = 9.6 \times 10^{-3}T\)

\(B_{min} = \frac{\mu_0Ni}{2\pi r_2}\)

\(= \frac{2\times10^{-7} \times800\times12}{0.25}\)

\(B_{min} = 7.6 \times10^{-3} T\)