Q. 55

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Found in: Page 833

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# The toroid of is a coil of wire wrapped around a doughnut-shaped ring (a torus). Toroidal magnetic fields are used to confine fusion plasmas.a. From symmetry, what must be the shape of the magnetic field in this toroid? Explain.b. Consider a toroid with N closely spaced turns carrying current I. Use Ampère’s law to find an expression for the magnetic field strength at a point inside the torus at distance r from the axis.c. Is a toroidal magnetic field a uniform field? Explain.

a. The shape of the magnetic field in this toroid, from symmetry is direction is counterclockwise.

b. An expression for the magnetic field strength at a point inside the torus at distance from the axis is .

c. The toroidal magnetic field a uniform field is Non- Uniform.

See the step by step solution

## Part (a) Step 1 : Given Information

We need to find the shape of the magnetic field in this toroid, from symmetry.

## Part (a) Step 2 :  Explanation.

The entry of the current is from the bottom side and out of the top side. Therefore we apply the right-hand rule, we can also find the magnetic field inside the toroid.

Counterclockwise, the magnetic field is distributed within the toroid and the space region enclosed by the toroid.

## Part (b) Step 1 : Given Information.

We need to find an expression for the magnetic field strength at a point inside the torus at a distance from the axis.

## Part (b) Step 2 : Simplifiy

This magnetic field tangent to circular path inside the toroid.

Out of the toroid, this field is zero because the current inside the coil is opposite to that outside the coil. therefore, the magnetic field is only in the space region inside the toroid. The turns of the coil, the net current is .

Solving equation () for B to get the magnetic field.

## Part (c) Step 1 : Given Information

We need to find the toroid magnetic field as a Uniform field.

## Part (c) Step 2 : Explanation.

The magnetic field of the toroid depends on the geometry of the toroid, it is non-uniform because changes and changes.