# Uniform magnetic field in a spherical region

• fysikgubbe
In summary, the conversation discusses the possibility of designing a current winding to produce a uniform magnetic field in a spherical region of space. A solenoid or Helmholtz coil can provide a uniform field, but not perfectly. It is possible in theory to generate a perfectly uniform B field from currents on the surface of a sphere, but the discontinuity at the surface must be taken into account. A boundary condition equation is available to address this issue.

## Homework Statement

Is it possible to design a current winding that will produce a uniform magnetic field in a spherical region of space?

## Homework Equations

Well, the literature tells that the equation for the B-field for a uniformly magnetized sphere = (2/3)u_0 * M and also the magnetization current density = J = curlM may be helpful.

## The Attempt at a Solution

The truth is that I don't even have a clue where to begin or how to think. Really need some help on this one.

What do you mean by "a uniform magnetic field in a spherical region of space"? Does the field have to be 0 outside the spherical region or something? If you just want a uniform field, a solenoid or Helmholtz coil can easily provide one. Define an arbitrary but small spherical region and you'd have a uniform field in a spherical region of space.

Neither a finite-length solenoid nor a Helmholtz coil produce a perfectly uniform field, even though both are widely used because their fields are uniform enough for many practical applications.

It is possible in theory to generate a perfectly uniform B field from currents on the surface of a sphere. I think you made a good start by realizing that a magnetized sphere has uniform B inside. The current density equation you wrote down, though, is appropriate for current inside the volume and you will need to deal with the discontinuity at the surface. This has been done for you already in the form of the boundary condition that gives equivalent surface current density at the material/air boundary. Take a look at that equation.

## 1. What is a uniform magnetic field in a spherical region?

A uniform magnetic field in a spherical region is a magnetic field that has the same strength and direction at all points within a spherical region. This means that the field lines are evenly spaced and parallel to each other.

## 2. How is a uniform magnetic field created in a spherical region?

A uniform magnetic field in a spherical region can be created by passing an electric current through a coil or solenoid that is placed inside the spherical region. This creates a magnetic field that is uniform within the region.

## 3. What is the significance of a uniform magnetic field in a spherical region?

A uniform magnetic field in a spherical region is important in many scientific and technological applications. It is used in MRI machines, particle accelerators, and in the study of magnetism and electromagnetism.

## 4. How does the strength of a uniform magnetic field in a spherical region vary with distance?

The strength of a uniform magnetic field in a spherical region does not vary with distance. This means that the magnetic field will have the same strength at any point within the region, regardless of the distance from the source.

## 5. Can a uniform magnetic field in a spherical region be manipulated or changed?

Yes, a uniform magnetic field in a spherical region can be manipulated or changed by changing the current or voltage in the coil or solenoid that creates the field. It can also be affected by the presence of other magnetic fields or magnetic materials within the region.