Question

The magnetic coils of a tokamak fusion reactor are in the shape ofa toroid having an inner radius of 0.700 m and an outer radius of1.30 m. The toroid has 860 turns oflarge-diameter wire, each of which carries a current of10.0 kA.

(a) Find the magnitude of the magnetic fieldinside the toroid along the inner radius.(b) Find the magnitude of the magnetic field inside the toroidalong the outer radius.

Answer 1

(a) 2.46 T

(b) 1.32 T

Step-by-step explanation:

Parameters given:

Inner radius of toroid,
`r_(in)` = 0.7 m

Outer radius of toroid,
`r_(out)` = 1.3 m

Number of turns in toroid, N = 860

Current in each turn, I = 10 kA = 10000 A

(a) The magnitude of the magnetic field inside the toroid along the inner radius is given as:

`B = (u_o * N * I)/(2\pi r_(in))`

where
`u_o =` magnetic permeability of free space

Therefore:

`B = (1.257 * 10^(-6) * 10000 * 860)/(2\pi * 0.7 ) \\\\\\B = 2.46 T`

(b) The magnitude of the magnetic field inside the toroid along the outer radius is given as:

`B = (u_o * N * I)/(2\pi r_(out))`

where
`u_o =` magnetic permeability of free space

Therefore:

`B = (1.257 * 10^(-6) * 10000 * 860)/(2\pi * 1.3 ) \\\\\\B = 1.32 T`