# Question #e7cf9

Mar 21, 2017

d) East

See below

#### Explanation:

The earth's magnetic field points South - North, ie the geographic North Pole is a south pole magnet-wise..... which is why the north pole of a compass points north.

We can now use the right hand rule to determine the direction of the force on a positively charged particle that is raining down on earth.

Problem is, there are a number of versions of the right hand (and left hand) rules.

I use this one because follows straight from the Lorentz Force Equation: $m a t h b f F = q \left(m a t h b f v \times m a t h b f B\right)$:

So, using your right hand:

• your forefinger points in the direction of travel of the positively charged particles (the old Benjamin Franklin idea of conventional current posits movement of positively charged particles). So you are pointing at the centre of the earth with that finger

• your middle finger points in the direction of the B field, ie South - North

Your thumb should now be pointing left - right .... or West - East if you were in outer space with the geographic North Pole of the earth pointing vertically upwards. That is the direction of the force on the particles.

However, in the UK at the 15- 16 yo level, you have Fleming's right (generators) and Fleming's left (motors) hand rules. And the fingers are pointing at different things.

If we think of this as a motor, ie it's as if the earth-bound particles were a moving current within a conductor, intended to power motion of the conductor, then we use Fleming's left hand rule, and the fingers point as follows:

We get the same result, of course:

• the forefinger points South - North, same as the earth's B- field

• the middle finger points at the centre of the earth, as that is the direction of travel of the positive charged particles

Once again, your thumb should now be pointing West - East.