# Effect of a magnetic field on a bean of particles.

• felixthecat
In summary, a beam of particles with charge q and velocity v is emitted from a point source at a small angle of angular dispersion with a magnetic field B. By using the equations F = qv x B and dv/dt = -q/m B x v, it can be shown that the magnetic field will focus the beam to a point at a distance z = 2πmv/|q|B. To solve the problem, one can use a Taylor approximation for the expression involving the angle between v and B, and calculate the location of a particle on the outer edge of the beam to determine where it will lie on the z-axis.
felixthecat

## Homework Statement

a beam of particles of charge q with velocity v is emitted from a point source, roughly parallel with a magnetic field B, but with a small angle of angular dispersion. Show that the effect of the field is to focus the beam to a point at a distance z = 2[/pi]mv/|q|B.

## Homework Equations

We know the force F= q vxB
dv/dt = -q/m Bxv

## The Attempt at a Solution

I try to solve the problem with the force. However, since the beam is roughly parallel to B, the cross product tends to 0. I am now like clueless...

The initial velocity is approximately parallel to B, not exactly parallel. Try calling the angle between v and B, $\theta$ and calculating r(t) for a particle on the beams outer edge. Then use a Taylor approximation for your expression for small $\theta$ to find the location where r(t) lies on the z-axis (assume that B points in the z-direction).

## What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be felt. It is created by moving electric charges and can be produced by magnets or electric currents.

## How does a magnetic field affect a beam of particles?

A magnetic field can cause a beam of particles to change direction or deflect from its original path. This is due to the magnetic force acting on the charged particles in the beam.

## What factors determine the strength of the effect of a magnetic field on a beam of particles?

The strength of the magnetic field, the charge and velocity of the particles in the beam, and the angle between the magnetic field and the direction of the beam all play a role in determining the effect of the magnetic field on the particles.

## Can a magnetic field be used to control a beam of particles?

Yes, a magnetic field can be used to control the direction and speed of a beam of particles. By adjusting the strength and direction of the magnetic field, the particles can be manipulated to follow a desired path.

## What applications does the effect of a magnetic field on a beam of particles have?

The effect of a magnetic field on a beam of particles has many practical applications, including particle accelerators, medical imaging, and cathode ray tubes in old television sets. It is also used in various research experiments in fields such as physics and chemistry.

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