# Forces on a proton

QUESTION:

A proton travelling due north enters a region that contains both a magnetic field and an electric field.
The Electric Field lines point due west. It is observed that the proton continues to travel in a straight line due north. In which direction must the magnetic field lines point?

Think of a plan view of the set up with N being towards the top of the page, W to the left, E to the left and S towards the bottom of the page. The proton enters from the bottom of the page and moves in a straight line towards the top.

It is not east because that is the direction that we want the force to act. For a magnetic field the force on a current (or a charged particle) is at right angles to the magnetic field direction.

Now the motion of a proton (positive charge) is the same as conventional current direction.

We need to have the force due to the magnetic field balance the force due to the electric field and so we need a force acting due east. This is the case because the force on the proton due to the electric field will act due west in the same direction as the electric field itself.

The force must be to the east, the current (initial motion of the proton) is due north and so, by Fleming's left hand rule, the magnetic field must act out of the paper, in other words UPWARDS.