# Magnetic field and a charge in room

1. Feb 23, 2012

### roboticmehdi

Imagine i am in a room in which there is a strong and homogeneous magnetic field ( strong B field ). and in the middle of the room the is a positively charged particle. the room is in space so there is no gravity to accelerate the particle downward, it just floats. since the particle is not moving the is no force on it and it is stationary. but now i start to move with little speed perpendicular to B lines. the charge experiences a force since it has relative velocity. How can that be? How can it experience a force just because im moving. and if i had a friend there who did not move with me he would say particle doesnt move and i would say it moves. how is that possible after all i am not moving at relativistic speed, only a few centimeters per second. how can we not agree with each other ? ( note: i purposely made magnetic field strong so that even little speed creates enormous force on particle, or imagine particle has huge charge so that again we have enormous force even at very little speed )

2. Feb 23, 2012

### Matterwave

If you are moving, the B-field will change from your perspective. The B-field is not an invariant, and changes depending on the motion of the observer. You will see a moving charge in a different B-field and E-field (depending on your motion and the direction of the B field) such that the effects cancel and the charge is not accelerated.

See here: http://en.wikipedia.org/wiki/Relativistic_electromagnetism

3. Feb 23, 2012

### stevenb

I think that you need to consider that you defined your static reference frame to be one with a uniform magnetic field in one direction, and zero electric field in all directions. However, once you move relative to this static frame, electric fields are not zero anymore. In your moving reference frame, you need to consider the total Lorentz force F=qE+vXB. I assume that if you do the transforms correctly, you will find zero net force on the charge in any inertial frame of reference.

Last edited by a moderator: Feb 23, 2012
4. Feb 23, 2012

### roboticmehdi

But Maxwell's equations must be valid in all frames of reference isn't that right? Why is it that I can use them safely for one reference frame, but for other frame of reference I have to supplement it with Einstein's special relativity ?

5. Feb 23, 2012

### Staff: Mentor

They are valid. You are neglecting that the field itself changes in your frame. If you moved to the left then both the field and the particle would then be moving at the same speed to the right from your view. Since the field isn't moving in relation to the particle, and the particle isn't moving in relation to the field, there is no force generated.

6. Feb 23, 2012

### stevenb

As said above, Maxwell's equations are valid in all frames. But, when you go from one frame to another, you have to transform the electric and magnetic fields appropriately. Electric and magnetic fields are not invariants. They are components of a 2nd rank tensor.

http://hepweb.ucsd.edu/ph110b/110b_notes/node69.html