# Forces on Charged Particles

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## Forces on Charged Particles

When a wire carrying a current through a field feels a force it is because the magnetic field pushes the electrons inside the wire to one edge of the wire. These electrons actually then apply force to the wire.

The same effect occurs if the electrons are not inside a piece of wire - for example, if they are in a beam crossing a vacuum.

We can calculate the force on a charged particle in a magnetic field using the equation:

F = B q v sin θ

Where:

F = force (N)

B = magnetic field strength (T)

q = charge on the particle (C)

v = velocity of the particle (m/s)

Note: Angle θ is between the direction of the beam and the magnetic field direction.

Use Fleming's left hand rule to work out the direction of the force. Align your second finger with the beam of particles remembering that it points the way positive particles flow, the opposite way to electron flow.

#### Finding the Charge-to-Mass Ratio of a Particle

When a charged particle enters a magnetic field we now know it will be forced to change direction. If it stays in the field it will continue to change direction and will move in a circle. The force produced will provide the centripetal force on the moving particle.

So:

This idea is used in velocity-selectors, where particles of different mass-to-charge ratio will rotate in circles with a different radius.