# Finding velocity of particles in a uniform magnetic field

• ILstudent122
In summary, the problem involves identical charged particles moving in a uniform electric field of 30,000 V/m and a uniform magnetic field of 10 T. The particles follow a straight line trajectory inside the capacitor and a circular trajectory outside the capacitor with a radius of 1 cm. The velocity of the particles is calculated to be 3000 m/s, but the mass of the particle is unknown. The equations E = F/q and r = mv/qB are possibly used to solve the problem. It is noted that the magnetic field is into the page and that the particles are in circular motion due to the velocity and magnetic force vectors. It is also mentioned that there are likely multiple forces acting on the particles while they are between the plates
ILstudent122

## Homework Statement

Given are a uniform electric field, E = 30,000 V/m inside a capacitor (see picture), and a uniform magnetic filed, B = 10 T, perpendicular to the plane of the page, present in all of the area.

Identical charged particles are moving in a trajectory marked by the dashed line, under the influence of the two fields: The trajectory inside the capacitor is a straight line, and the trajectory outside the capacitor is circular, with radius r = 1 cm.

What is the velocity v of the charged particles?

## Homework Equations

Possibly r = mv / qB , but I don't know the mass of the particle.
Maybe E = F/q

## The Attempt at a Solution

I know that the magnetic field is into the page based on the RHR. The particle is in circular motion because of the velocity and magnetic force vectors. The answer is v = 3000 m/s but I have no idea how it was derived.

How many forces act on the particles while they are between the plates of the capacitor?

What can you say about these forces given the fact that the particles are traveling in a straight line with a constant speed between the plates?

Just noticed that this is your first post at PhysicsForums, ILstudent122. Welcome!

Last edited:

## What is a uniform magnetic field?

A uniform magnetic field is a magnetic field that has the same strength and direction at every point in space. This means that the field lines are parallel and evenly spaced, creating a constant force on any particles within the field.

## How do you find the velocity of particles in a uniform magnetic field?

The velocity of particles in a uniform magnetic field can be found using the formula v = (q/m) * B * r, where q is the charge of the particle, m is the mass of the particle, B is the strength of the magnetic field, and r is the radius of the particle's circular motion within the field.

## What factors affect the velocity of particles in a uniform magnetic field?

The velocity of particles in a uniform magnetic field is affected by the strength of the magnetic field, the charge and mass of the particles, and the radius of their circular motion within the field. Any changes in these factors will result in a change in the velocity of the particles.

## How does a uniform magnetic field affect the motion of charged particles?

A uniform magnetic field causes charged particles to move in a circular path because the force exerted by the field acts perpendicular to the velocity of the particles. This results in a constant centripetal force that keeps the particles moving in a circular motion within the field.

## Can the velocity of particles in a uniform magnetic field be controlled?

Yes, the velocity of particles in a uniform magnetic field can be controlled by changing the strength of the magnetic field or by adjusting the charge, mass, or radius of the particles. This allows for precise manipulation of the particles' motion within the field.

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