Moving in a Circle

If a charged particle enters a magnetic field it will feel a force. We now know the size of the force (given by equation above) and direction of the force (given by Fleming’s Left Hand Rule).

If we use the left hand rule in the diagram to the right we can see that the force is always at right angles to the velocity. First finger points into the page, middle finger points along the line and our thumb points upwards.

While the particle is in the magnetic field it will move in a circle.

Radius of the circle

We can calculate the radius a charged particle will move in by using our equation for the force on a charged particle in a magnetic field and a centripetal force equation.

and are equal to each other so we can write

Time for a complete circle

We can also calculate the time it takes for the charged particle to move in one complete circle.

Starting at we can use to make the equation become and then

The centripetal force is due to the magnetic force on the charged particle so we can put these equal to each other. cancel the v to become which rearranges to:

So the time it takes to complete a full circle does not depend on the velocity.