# Stationary Electron in changing magnetic field

• perryizgr8
In summary, we discussed the effects of a time-varying magnetic field on a stationary electron. While a stationary electron in a uniform magnetic field experiences no force, a changing magnetic field can produce an electric field which can accelerate free electrons or work on an electron's spin magnetic momentum. In the case of a single charged particle, the induced emf and subsequent force can be calculated by multiplying the rate of change of magnetic field with the area of a loop. Additionally, in vector analysis, "rot E" refers to the rotation of the electric field.
perryizgr8
I know that a stationary electron kept in uniform magnetic field experiences no force. But will it experience force if the field suddenly starts varying with time?
Any help will be appreciated.

Certainly. Faraday's Law of induction produces an electric field near (as well as in) a rapidly changing magnetic field. The secondary winding of a transformer is an example. In vacuum, a changing magnetic field can accelerate free electrons. The betatron electron (particle) accelerator accelerates electrons by the electric (Faraday induction) field due to a changing magnetic field.
Bob S

Hi.

rot E = -∂B/∂ｔ. Electric field E induced by time-varying magnetic field B works on the electron.

F = m・grad B. In case of space-varying magnetic field, magnetic force also works on electron with spin magnetic momentum m.

Regards.

Hi. Thanks for the replys. Sweet spring, I'm viewing with my phone and don't have access to a computer right now and I can't see the formulas that you wrote. Can you rewrite them without using special characters?
Usually to calculate induced emf I multiply dB/dt with the area of a loop. But when there is only a single charged particle what do I do to get the emf and subsequentally the force on the particle?
Also what does 'rot E' mean?

Last edited:
Hi. Let me explain in some specific case. Magnetic flux Φ is bundled in the rod shape and change in time. Outside of the bundle, B = 0 and induced electric field E appears in tangent direction of a circle around the bundle. E works force on an electron there. Not only time but also space variation of B is required in this case. I assume it is so in general case.

rot is the abbreviation of ”rotation” in vector analysis.

Regards

## What is a stationary electron in a changing magnetic field?

A stationary electron in a changing magnetic field refers to a situation where an electron is held in place while a magnetic field around it is changing. This can occur in a variety of settings, such as in a laboratory experiment or in a magnetic field generated by a moving object.

## How does the motion of a stationary electron change in a changing magnetic field?

The motion of a stationary electron in a changing magnetic field is governed by the Lorentz force, which is perpendicular to both the direction of the electron's motion and the direction of the magnetic field. This results in the electron being pushed in a circular path around the magnetic field lines.

## What is the significance of a stationary electron in a changing magnetic field?

Studying the behavior of a stationary electron in a changing magnetic field is important for understanding the principles of electromagnetism and the behavior of charged particles in magnetic fields. It also has practical applications in fields such as electronics and particle accelerators.

## What factors affect the motion of a stationary electron in a changing magnetic field?

The strength and direction of the magnetic field, the charge and mass of the electron, and the speed of the electron all play a role in determining the motion of a stationary electron in a changing magnetic field. External forces, such as electric fields, can also affect the electron's motion.

## What is the difference between a stationary electron in a changing magnetic field and a moving electron in a constant magnetic field?

In a stationary electron in a changing magnetic field, the electron remains in the same location while the magnetic field around it changes. In contrast, a moving electron in a constant magnetic field experiences a continuous force that causes it to move in a circular path around the magnetic field lines.

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