# An Electrostatics Question

1. Jul 17, 2007

### Sleek

1. The problem statement, all variables and given/known data
The problem is a Multiple Choice Question, as follows.

Q: An electron moves with a constant velocity in an electric field. What could its direction of motion be?

1> Parallel To Field's Direction
2> Anti-Parallel To Field's Direction
3> Perpendicular To Field's Direction
4> Any Other Direction Than The Above

2. Relevant equations

$$F=\frac{1}{4\pi\epsilon_0}\frac{q_1 q_2}{r^2}$$

3. The attempt at a solution

This problem's solution is known to me. But for some reason, I and my teacher disagree. I'll explain both of our explanations. I haven't conveyed my explanation to my teacher yet, as I didn't get a chance to meet him.

Anti-Parallel, i.e. from negative to positive. The reason for this being, an electron is negatively charged. Thus it has a tendency to move from negative to positive. And thus that will be its direction.

My Argument:

If the electron moves from negative to positive, there is a force of interaction between the positive terminal and the electron. As the electron is moving towards it, a component of the force would act along the direction of the electron, thus accelerating it. It won't be moving with constant velocity.

The above reasoning might be a misunderstanding of mine, but still, I'd be better to get it cleared.

Perpendicular. Since the electron is moving perpendicular to the field with const. velocity, the force acting "upwards" is 0, while 90 degrees towards its sides is some value, depending upon the magnitude of the field. Thus, only the direction of the electron would change, and its velocity would remain constant. It'd follow somewhat a parabolic path.

I'd like to know your opinion, so that I can realize where my thinking was actually flawed. Its really better to understand things before moving on to more complex stuff.

Thanks!,
Sleek.

Last edited: Jul 17, 2007
2. Jul 17, 2007

### nrqed

Are you sure it is moving in an electric field and not a magnetic field? And are you sure that the question says that the velocity is constant (as opposed to the speed)? There is no way a charge can move in an electric field without the velocity changing (this is only possible if either the charge or the field is zero)

3. Jul 17, 2007

### Sleek

Yes, the charge is present in a uniform electric field. The question precisely mentions velocity, though I think it refers to speed instead. Thus, the direction change doesn't matter, just the speed should remain constant.

Regards,
Sleek.

Last edited: Jul 17, 2007
4. Jul 17, 2007

### nrqed

:surprised At what level is this? This is a physics professor?

The sentence "Thus it has a tendency to move from negative to positive." makes no sense at all. An electron released from rest will move opposite to an E field but that's totally irrelevant to the question.

An electron feels a force opposite to the direction of the electric field. So an electron moving opposite to the E field will speed up in that direction.

Quite right. You seem to understand the situation better than your prof.

The flaw in your answer is that if the direction changes, the velocity changes too. Because velocity includes direction and magnitude!

5. Jul 17, 2007

### nrqed

Ah, that changes everything. In that case, you are correct. Momentarily , the speed won't change at the instant the electron is moving perpendicular to the field. That is just true momentarily but is indeed the correct answer. I am really surprised by what your prof said.

6. Jul 17, 2007

### Sleek

Yes, I'm aware that the speed won't remain constant for long. Because at some point (assuming the field is quite large), the motion of electron will be such directed that there will be a component of force along its direction of motion.

7. Jul 18, 2007

### nrqed

Exactly.

So the initial question was posed incorrectly.