Question

Replace the current loops of Question 8 and Fig. 32-24 with diamagnetic 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?

Short answer

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

Step-by-step solution

Given

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

The uniform external magnetic field for sphere 3

Determining the concept

When a diamagnetic sphere is placed in an external magnetic field, it develops a magnetic dipole moment in the direction opposite to that of the external magnetic field.

The magnetic dipole moment is the difference between the North Pole and the South Pole. The electron of an atom and circular current loop too has a magnetic dipole moment.

(a) Determining the direction of the magnetic dipole moment of the diamagnetic spheres

• A diamagnetic material does not have a net magnetic dipole moment. When it is placed in an external magnetic field, it develops a net magnetic dipole moment, but the direction is opposite to that of the external magnetic field.
• For the first two spheres, the external magnetic field is directed downwards. Hence the direction of the magnetic dipole moment is upward.
• For the third sphere, the direction of the external magnetic field is upwards. Hence the direction of the dipole magnetic moment is downward.
• Therefore, the direction of the magnetic dipole moment of the diamagnetic spheres is 1-upward, 2- upward, and 3-downward.

(b) Determining the direction of the magnetic force on the diamagnetic spheres

• When the external magnetic field surrounding the diamagnetic sphere is non-uniform, it is repelled from the region of the greater magnetic field towards 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 towardsthelower region, i.e., downwards.
• 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 towardstheupper region, i.e., upwards.
• 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-downward, 2- upward, 3- zero.
• The diamagnetic substance does not have a net magnetic dipole moment. It develops a dipole moment when placed in an external magnetic field. Its direction is opposite to that of the external field. In the non-uniform field, it experiences a force towards the lower magnitude of the field.