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Found in: Page 966

### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# Replace the current loops of Question 8 and Fig. 32-24 with paramagnetic spheres. For each field, are (a) the magnetic dipole moment of the sphere and (b) the magnetic force on the sphere directed up, directed down, or zero?

1. The direction of the magnetic dipole moment of the paramagnetic spheres is 1-downward, 2- downward, and 3-upward.
2. The direction of the magnetic force on the diamagnetic spheres is 1-upward, 2- downward, and 3- zero.
See the step by step solution

## Step 1: Given

The non-uniform external magnetic field for spheres 1 and 2.

The uniform external magnetic field for sphere 3.

## Step 2: Determining the concept

Paramagnetic materials have atoms with a permanent magnetic dipole moment, but they are randomly oriented. Thus they have no net moment. When a paramagnetic sphere is placed in an external magnetic field, magnetic dipoles tend to align in the direction of the external magnetic field.

## Step 3: (a) Determining the direction of the magnetic dipole moment of the paramagnetic spheres

A paramagnetic material does not have a net magnetic dipole moment as the atomic moments are randomly oriented. When it is placed in an external magnetic field, the moments tend to align with the external magnetic field. Hence its net magnetic dipole moment is along the direction of the external field.

For the first two spheres, the external magnetic field is directed downwards. Hence the direction of the magnetic dipole moment is also downward.

For the third sphere, the direction of the external magnetic field is upwards. Hence the direction of the dipole magnetic moment is also upward.

Therefore, the direction of the magnetic dipole moment of the paramagnetic spheres is 1-downward, 2- downward, and 3-upward

## Step 4: (b) Determining the direction of the magnetic force on the paramagnetic spheres

When the external magnetic field surrounding the paramagnetic sphere is non-uniform, it is attracted towards the region of the greater magnetic field from the region of the lesser magnetic field.

For sphere 1, the magnetic field is greater in the upper part of the sphere than that in the lower part. Hence the magnetic force will be directed towards the upper region, i.e., upwards.

For sphere 2, the magnetic field is greater in the lower part of the sphere than that in the upper part. Hence the magnetic force will be directed towards the lower region, i.e., downwards.

For sphere 3, the external magnetic field is uniform; hence the force acting on the sphere is zero.

Therefore, the direction of the magnetic force on the diamagnetic spheres is 1-upward, 2- downward, 3- zero.

The paramagnetic substance does not have a net magnetic dipole moment as the atomic moments are randomly oriented. It develops a dipole moment when placed in an external magnetic field because the moments tend to align themselves along the direction of the external field. In a non-uniform field, it experiences a force towards the region of the greater magnitude of the field.