# Homework Help: Show the drift velocity is ExB/B^2

1. Mar 26, 2016

### shedrick94

• HW Template missing as it was moved from another forum
A charged particle drifts in uniform, constant magnetic and electric fields. The electric field, E, is perpendicular to the magnetic field, B.

Show that the drift velocity is given by vd = (E×B)/B2

Heres where I get to:
F=e(E+vxB)=0 as v is uniform.

Therefore E+vxB=0.

Take vector product of B with both sides.

BxE +Bx(vxB)=0.

Using identity Ax(BxC) = B(A.C)-C(A.B)

I get BxE+v(B.B)-B(B.v)=0
Then I don't know where to go from here.

2. Mar 26, 2016

### Staff: Mentor

You can assume that the drift happens in two dimensions, so you can say something about the relative direction of v and B which simplifies (B.v).
In three dimensions the total velocity does not have to follow the initial equation, so you need that assumption.

3. Mar 26, 2016

### shedrick94

Why are you allowed to assume the drift is in two dimensions though?

4. Mar 26, 2016

### Staff: Mentor

The component in the third dimension is not a drift.

5. Mar 26, 2016

### shedrick94

Would that be an acceleration then?

6. Mar 26, 2016

### Staff: Mentor

A motion in the third direction would stop quickly in matter. In vacuum, the charged particle could freely keep moving in that direction, without influencing the two-dimensional motion in the other directions.

7. Mar 26, 2016

### shedrick94

Can I ask what it means by a drift velocity then?

8. Mar 26, 2016

### Staff: Mentor

The velocity in the two-dimensional plane I mentioned.

9. Mar 26, 2016

### shedrick94

yes but what does it specifically mean by 'drift'. You said the velocity in the 3rd dimension is not a drift.

10. Mar 26, 2016

### Staff: Mentor

I guess it is just convention to call that drift.