The magnetic coils of a tokamak fusion reactor are in theshape of a toroid having an inner radius of 0.900 m and an outer radiusof 1.60 m. The toroid has 800 turns of large-diameter wire, each of whichcarries a current of 18.0 kA. Find the magnitude of the magnetic fieldinside the toroid along (a) the inner radius and (b) the outer radius.

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Asked Sep 23, 2019
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The magnetic coils of a tokamak fusion reactor are in the
shape of a toroid having an inner radius of 0.900 m and an outer radius
of 1.60 m. The toroid has 800 turns of large-diameter wire, each of which
carries a current of 18.0 kA. Find the magnitude of the magnetic field
inside the toroid along (a) the inner radius and (b) the outer radius.

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Expert Answer

Step 1

Ampere’s circuital law can be used to find the magnitude of the magnetic field. The law is given by

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B-dl N Here, B is the magnetic field, dl is the infinitesimal line element of the coil, N is the mumber of turns of the coil, is the absolute permeability and I is the enclosed current The angle between the magnetic field and the line element is zero so that Bdl NI вбаі - Nн,1 The value of the integral in the above equation will be the perimeter of the toroid в(2лr) %3 NuJ NI В - 2π (1) The value of is 47x10 H/m

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Step 2

(a)Substitute the numerical values in equation (1) for the ...

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(800) (47 x 107 H/m)(18.0x103 A) B = 27 (0.900 m =3.2 T (b) Substitute the numerical values in equation (1) for the magnetic field along the outer radius of the toroid (800) (4,7x107 H/m)(18.0x10 A) 2π(1.60 m) B = =1.8 T

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Magnetic Effects of Current

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