# Kinetic energy of electron in non-uniform B?

• jason12345
In summary, the kinetic energy of an electron in a non-uniform magnetic field will increase just like a bar magnet due to the Lorentz force acting on its charged nature. This is supported by experimental evidence and is why magnets are used for applications such as plasma containment and fusion reactors. However, in a uniform magnetic field, the electron will only experience a torque and not a net force on its center of mass, resulting in no change in kinetic energy.
jason12345
The kinetic energy of a bar magnet changes in a non-uniform magnetic field so is there experimental evidence that this is true for the kinetic energy of an electron since it possesses an intrinsic magnetic moment?

Any charged particle will react to a magnetic field because it is charged, not because it has a magnetic moment. In fact, the magnetic moment only exists because it is charged. The fact that you can apply a force on an electric charge is the reason we use magnets for things like plasma containment and fusion reactors.

Drakkith said:
Any charged particle will react to a magnetic field because it is charged, not because it has a magnetic moment. In fact, the magnetic moment only exists because it is charged. The fact that you can apply a force on an electric charge is the reason we use magnets for things like plasma containment and fusion reactors.

Yes, a static magnetic field will change the momentum of an electron and we're told also that it doesn't do work either so the electron's kinetic energy remains constant. On the other hand, a non-uniform magnetic field causes the centre of mass of a bar magnet to accelerate with the kinetic energy coming from the magnet. Does this mean that an electron will have a linear acceleration also?

Yep, the electron will accelerate.

Drakkith said:
Yep, the electron will accelerate.

I didn't express myself correctly. Yes it will accelerate, as all charged particles do in magnetic fields. Place a macroscopic magnetic dipole like a bar magnet in a uniform magnetic field and it will experience a torque, but no net force on its centre of mass. Put it in a non-uniform magnetic field and the centre of mass will accelerate with an increase in kinetic energy.

If an electron is put in a uniform magnetic field, it accelerates from the Lorentz force. Put it in a non-uniform magnetic field and does its kinetic energy increase like that of the bar magnet?

## 1. What is the formula for calculating the kinetic energy of an electron in a non-uniform magnetic field?

The formula for calculating the kinetic energy of an electron in a non-uniform magnetic field is KE = eB/2mc * (vperp)2, where e is the charge of an electron, B is the magnetic field strength, m is the mass of the electron, and vperp is the velocity of the electron perpendicular to the magnetic field.

## 2. How does the kinetic energy of an electron change in a non-uniform magnetic field?

The kinetic energy of an electron in a non-uniform magnetic field will change if the magnetic field strength or the velocity of the electron changes. If the magnetic field strength increases, the kinetic energy will also increase. Similarly, if the velocity of the electron increases, the kinetic energy will also increase.

## 3. What is the relationship between the magnetic field strength and the kinetic energy of an electron in a non-uniform magnetic field?

The kinetic energy of an electron in a non-uniform magnetic field is directly proportional to the magnetic field strength. This means that if the magnetic field strength doubles, the kinetic energy of the electron will also double.

## 4. Can the kinetic energy of an electron in a non-uniform magnetic field ever be negative?

No, the kinetic energy of an electron in a non-uniform magnetic field can never be negative. This is because kinetic energy is a measure of how much energy an object has due to its motion, and it is always a positive value.

## 5. Does the direction of the magnetic field affect the kinetic energy of an electron in a non-uniform magnetic field?

Yes, the direction of the magnetic field can affect the kinetic energy of an electron in a non-uniform magnetic field. If the magnetic field is parallel to the motion of the electron, the magnetic force will not do any work on the electron and the kinetic energy will remain constant. However, if the magnetic field is perpendicular to the motion of the electron, the magnetic force will do work on the electron and the kinetic energy will change.

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