# Magnetic Force on a Charged Particle in Constant Magnetic Field

• arod2812
In summary, a charged particle moving in a uniform, constant magnetic field is the topic of discussion. The conversation focuses on determining the false statement about the magnetic force exerted on the particle. The last statement, "it does no work on the particle," is deemed as the correct answer. The reason for this is because a static magnetic field, which exerts a force on a charged particle, cannot do work as the force and velocity are always perpendicular to each other.
arod2812

## Homework Statement

A charged particle is moving in a uniform, constant magnetic field. Which one of the following statements concerning the magnetic force exerted on the particle is false?
It changes the velocity of the particle.
It increases the speed of the particle.
It does not change the kinetic energy of the particle.
It can act only on a particle in motion.
It does no work on the particle.

## Homework Equations

Could you explain why it false?

## The Attempt at a Solution

I am told that the answer is the last one.

3. The Attempt at a Solution
I am told that the answer is the last one.
Not really an attempt!

This isn't obvious but a static magnetic field, whose force on a charge particle is given by F=q(VxB), can not do work.

Remember that work in general depends on the direction between the applied force and the direction of motion. If they're in the same direction then you get the simple W=F*d, and slightly more generally, W=F*d*cos(theta) where theta is the angle between them.(because really it's a dot product)

So now look at the equation for force, and tell me, knowing the definition of a cross product, if the force vector will ever be anything but perpendicular to the velocity of the particle? What's the result of that?

mgb_phys said:
Not really an attempt!

## What is the magnetic force on a charged particle in a constant magnetic field?

The magnetic force on a charged particle in a constant magnetic field is the force exerted on the particle due to its motion in the presence of the magnetic field. It is perpendicular to both the particle's velocity and the magnetic field.

## How is the magnetic force calculated?

The magnetic force on a charged particle in a constant magnetic field can be calculated using the formula F = qvBsinθ, where q is the charge of the particle, v is its velocity, B is the strength of the magnetic field, and θ is the angle between the velocity and the magnetic field.

## What is the direction of the magnetic force?

The direction of the magnetic force is perpendicular to both the velocity of the charged particle and the magnetic field. This direction can be determined using the right-hand rule, where the thumb points in the direction of the particle's velocity, the index finger points in the direction of the magnetic field, and the middle finger points in the direction of the magnetic force.

## How does the magnetic force affect the motion of a charged particle?

The magnetic force causes a charged particle to move in a circular or helical path, depending on the initial velocity and the strength of the magnetic field. This is because the magnetic force is always perpendicular to the velocity, resulting in a change in direction but not in speed.

## What factors affect the strength of the magnetic force on a charged particle?

The strength of the magnetic force on a charged particle is affected by the particle's charge, velocity, and the strength and direction of the magnetic field. The angle between the velocity and the magnetic field also plays a role, as the force is strongest when the angle is 90 degrees.

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