Auniform magnetic field is directed horizontally towards the east, and a negative charge is moving east through this magnetic field. in what direction, if at all, is the magnetic force on the particle?

No

Explanation:

There is no magnetic force on the charge.

The negative charge is moving towards east and the direction of magnetic field is also towards east.

So both velocity and direction of field is same there will be no magnetic field.

as per the equation of magnetic force,

                                                  F = qvB sin θ

here θ is the angel between the direction of field and direction of movement of charge which is 0 in this case.

Now value of Sin 0 = 0

Therefore Force = 0 ; Hence there will be no magnetic force on the particle.