Electromagnetism question, what formula

1. Dec 15, 2009

fluidistic

I'd like to know what formula to use in order to find the following :
Imagine a uniform magnetic field. I am moving with a constant velocity perpendicularly through it. Do I see only an electric field? A magnetic field? Both? Or both of them?
What if I move in the sense of the magnetic field with a constant velocity?

What if my velocity changes with time?
What if, instead of the magnetic field, it's an electric field?

I do not expect the answer to all these questions, rather I'd like a formula to check it out myself. But if you have to say a word or even give the answer, I'm all ears.

2. Dec 15, 2009

Pythagorean

What velocity are you traveling with? If it's much lower than the speed of light:

3. Dec 15, 2009

fluidistic

Thanks a lot. I'm a bit confused, if B is uniform, if I move, $$\frac{\partial B}{\partial t}=0$$ or I'm wrong?

4. Dec 15, 2009

Staff: Mentor

5. Dec 15, 2009

fluidistic

6. Dec 15, 2009

kcdodd

To look at EM in another velocity you need to use a lorentz transformation of the field. If you are familiar with vectors, J.D. Jackson p. 558 gives a useful form:

$$\vec{E}' = \gamma (\vec{E} + \vec{\beta} \times \vec{B}) - \frac{\gamma^2}{\gamma + 1} \vec{\beta} (\vec{\beta} \cdot \vec{E})$$

$$\vec{B}' = \gamma (\vec{B} - \vec{\beta} \times \vec{E}) - \frac{\gamma^2}{\gamma + 1} \vec{\beta} (\vec{\beta} \cdot \vec{B})$$

$$\vec{\beta} = \vec{v}/c$$
$$\gamma = \frac{1}{\sqrt{1 - \beta^2}}$$

So, you see if you have one frame where E = 0, and only B != 0. Then in every other frame E' != 0, and B' != 0, since B appears in both terms.

7. Dec 15, 2009

fluidistic

Ok thank you very much. I'm going to try to grasp this. I took vector calculus. I'm taking the 1 year EM course on next term (in March). I thought I would need it for the intro to EM course, but I'm not sure now. Anyway, I'll do an effort to learn this part.