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.