How can the force from the magnetic field depend on the velocity of a charge since velocity is relative?

Question

I learned in Physics class that the force from a magnetic field on a charged particle is: F = q v x B. Where v and B are the velocity and magnetic field vectors, q is the charge and x means cross product. But, the velocity depends on my frame of reference. For instance I could be moving at the same velocity as the particle so that the particle appears to be stationary in my frame of reference. The force on the particle can't change just because my velocity changes. If it did then different observers would see something different. I'm obviously missing something here.

Answer 1

You're forgetting the other side of the equation!

Yes, you are moving with the particle. But now you're moving with respect to the field! So this relative motion still produces a force. To wit: There will be a force if the field rapidly passes over you while you "sit still."

This is similar to the way induction works. Induction works whether you pass a magnet through a coil, or a coil over a magnet. All that matters is the relative motion of the field and the charge, and the relative motion is conserved, no matter what frame you're in. Since the relative motion is the same, the force is the same.

Answer 2

As you noticed in the equation, B does not have any velocity attached to it. This means that the Magnetic field has to be stationary for the equation to work. If you are moving relative to the reference frame of the magnetic field, the equation does not apply anymore.

Answer 3

first of all, Amal Raj is thoroughly wrong. E does not equivalent -vb or -qvB. those are expressions for the tension a advantageous test particle will expertise in a magnetic field, and that's almost Ampere's regulation. all people who says you prefer Maxwell's equations to respond to this question is stable. You do. There are 4, anybody has already long long previous to the venture of itemizing them and there is you're respond. carry in mind that each B and H make certain the energy in a magnetic area, in accordance to the 4 Maxwell's equations. And the two are vector parts, as is E the electrical powered field, additionally a vector. in basic terms suited success with your income information of of electrodynamics. this is a complicated subject. John

Answer 4

You aren't missing anything--you are stumbling on one of the problems with electricity and magnetism--the fundamental laws are not invariant under the old galilean relativity. Reconciling them requires special relativity, in which you view the E-field and the B-field as parts of the same field in 4-d space time. What looks like a B-field to one observer looks like an E-field to another. Special relativity gives you the recipes to get back and forth.