# Charge passing through a magnetic field of uniform magnetic flux density

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1. Apr 5, 2015

### 3OPAH

My reasoning:

The magnetic force on charge q is

Fm = qv x B

B does not change |v|. Therefore, |Fm| is constant at time t > 0 and Fm is always perpendicular to the direction of movement of charge q. Fm behaves as a centripetal force, and thus the charge moves along the circumference of a circle.

Here is my drawing depicting what I think is happening:

Now, knowing that an electric charge q either at rest or in motion, experience an electric force Fe in the presence of an electric field E, that is,

Fe = qE

Then if we have a charge q moving with velocity v in the presence of both an electric field E and a magnetic flux density B, the total force exerted on the charge is therefore

F
= Fe + Fm = q(E + v x B)

which is the Lorentz force equation.

I am having trouble using what I have done so far and what I know about the magnetic force and electric force to compute the necessary electric force needed to make charge q move in a straight line. If the charge is moving in a circular path about the xy-plane under the influence of a magnetic field in the positive z direction, then the necessary electric field needed to counteract the circular movement of the charge and make it move in a straight line will be a combination of x and y coordinates, correct?

2. Apr 5, 2015

### Staff: Mentor

Correct.

What is the net force on the charge if it moves in a straight line at constant speed*?

*this is not required, but if you allow a variable speed things get really messy

3. Apr 5, 2015

### 3OPAH

If a charge experiences no net force, then its velocity is constant; the charge is either at rest (if its velocity is zero), or it moves in a straight line with constant speed. So the net force is zero.

4. Apr 5, 2015

Right.

5. Apr 5, 2015

### 3OPAH

So we are given the initial velocity of v = aex + bey. The magnitude of the velocity vector has to be the same, but opposite in direction. So the necessary electric field is (with the magnetic flux density in there as well):

E = -bB_0ex + aB_0ey

correct?

6. Apr 5, 2015

Correct.