Non-uniform Magnetic Field

Definition

A non-uniform magnetic field is a magnetic field where the strength and/or direction of the magnetic flux varies across a given region of space. This is in contrast to a uniform magnetic field, where the magnetic flux is constant throughout the space.

5 Must Know Facts For Your Next Test

1. In a non-uniform magnetic field, the force experienced by a current-carrying loop or a magnetic dipole will depend on the orientation of the loop or dipole relative to the field.
2. The torque experienced by a current-carrying loop in a non-uniform magnetic field will be proportional to the magnetic gradient and the area of the loop.
3. Non-uniform magnetic fields are commonly used in devices such as electric motors, generators, and magnetic resonance imaging (MRI) machines.
4. The force and torque experienced by a current-carrying loop in a non-uniform magnetic field can be used to measure the strength and direction of the magnetic field.
5. The motion of charged particles in a non-uniform magnetic field can be used to separate and analyze different isotopes or particles in mass spectrometry and other applications.

Review Questions

• Explain how the force experienced by a current-carrying loop in a non-uniform magnetic field depends on the orientation of the loop.
  • In a non-uniform magnetic field, the force experienced by a current-carrying loop will depend on the orientation of the loop relative to the field. If the loop is aligned with the magnetic field, the force will be zero. However, if the loop is not aligned with the field, there will be a force that acts to align the loop with the field. The magnitude of this force will be proportional to the magnetic gradient and the area of the loop, as well as the current flowing through the loop.
• Describe how the torque experienced by a current-carrying loop in a non-uniform magnetic field is related to the magnetic gradient and the area of the loop.
  • The torque experienced by a current-carrying loop in a non-uniform magnetic field is proportional to the magnetic gradient and the area of the loop. Specifically, the torque is given by the cross product of the magnetic moment of the loop (which is the product of the current and the area of the loop) and the magnetic gradient. This means that the torque will be maximized when the loop is oriented perpendicular to the direction of the magnetic gradient, and will be zero when the loop is aligned with the gradient.
• Evaluate the importance of non-uniform magnetic fields in practical applications, such as electric motors, generators, and MRI machines.
  • Non-uniform magnetic fields play a crucial role in many practical applications. In electric motors and generators, the non-uniform magnetic field created by the rotor and stator windings generates the torque that drives the rotation of the motor or generator. In MRI machines, the non-uniform magnetic field, combined with radio frequency pulses, is used to generate detailed images of the body's internal structures by exciting and detecting the resonance of hydrogen protons in the tissues. The ability to precisely control and measure non-uniform magnetic fields is essential for the proper functioning of these and other important devices that rely on the interaction between magnetic fields and current-carrying loops or magnetic dipoles.

Related terms

Magnetic Flux: The measure of the total magnetic field passing through a given surface or area.

Magnetic Gradient: The rate of change of the magnetic field strength with position in a specific direction.

Torque:

The rotational force that causes an object to rotate about an axis, fulcrum, or pivot.