# Understanding Work Done in a Bfield on an Electron

• chiddler
In summary, magnetic forces do not do work on particles because the force is always perpendicular to the field. However, when a particle is constrained to a bar and forced to move in one direction, the magnetic field can create work on the particle. This is because the particle is no longer able to escape the force and is forced to move along the bar's path, resulting in the magnetic forces exerting work on it.
chiddler

## Homework Statement

Magnetic forces do no work because all the force is perpendicular to movement.

A bar is moving in a Bfield. "How much work is done on an electron moving across the bar?"

Why is there work in this case?

## Homework Equations

F = qvBsin(θ)
W = Fd = qvBd*sin(θ)

## The Attempt at a Solution

Thanks very much.

My friend provided a helpful response:

Because the particle is constrained to the bar. Magnetic forces do no work on particles because the force on the particle is always perpendicular to the field. When the particle is trapped in a bar and is forced to move in one direction only, the magnetic field creates a constant force in one direction only, that means it DOES create work. Think of it this way, in a spherical field, a particle will always be pushed away from the curve of the field itself, meaning its always a centripetal force, meaning its always perpendicular to the movement of the particle. Now if you restrain that particle into a bar, the force may come at various angles to it, but now the particle can't escape and thus moves along the bar path, meaning the forces start to apply some work.

:-3

## What is "work" in the context of a B-field and an electron?

"Work" is a measure of the energy transferred to or from an object due to a force acting on it. In the context of a B-field and an electron, work refers to the energy gained or lost by the electron as it moves through the B-field.

## How is work done on an electron in a B-field calculated?

The work done on an electron in a B-field can be calculated using the formula W = qvBd, where q is the charge of the electron, v is its velocity, B is the strength of the B-field, and d is the distance the electron travels in the B-field.

## What happens to the work done on an electron in a B-field?

The work done on an electron in a B-field is converted into kinetic energy, causing the electron to either speed up or slow down depending on the direction of the B-field and the direction of the electron's motion.

## How does the direction of the B-field affect the work done on an electron?

The direction of the B-field determines the direction of the force exerted on the electron, which in turn determines the direction of the work done on the electron. If the B-field is perpendicular to the electron's motion, the work done will be at its maximum. If the B-field is parallel to the electron's motion, no work will be done.

## What is the significance of understanding work done on an electron in a B-field?

Understanding work done on an electron in a B-field is important in many applications, such as particle accelerators, electric motors, and generators. It also helps in understanding the behavior of charged particles in magnetic fields, which is crucial in fields such as plasma physics and astrophysics.

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