Answer:
(a) 2.46 T
(b) 1.32 T
Explanation:
Parameters given:
Inner radius of toroid, [tex]r_{in}[/tex] = 0.7 m
Outer radius of toroid, [tex]r_{out}[/tex] = 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:
[tex]B = \frac{u_o * N * I}{2\pi r_{in}}[/tex]
where [tex]u_o =[/tex] magnetic permeability of free space
Therefore:
[tex]B = \frac{1.257 * 10^{-6} * 10000 * 860}{2\pi * 0.7 } \\\\\\B = 2.46 T[/tex]
(b) The magnitude of the magnetic field inside the toroid along the outer radius is given as:
[tex]B = \frac{u_o * N * I}{2\pi r_{out}}[/tex]
where [tex]u_o =[/tex] magnetic permeability of free space
Therefore:
[tex]B = \frac{1.257 * 10^{-6} * 10000 * 860}{2\pi * 1.3 } \\\\\\B = 1.32 T[/tex]
