# Is Principle of Relativity compatible with Magnetic force

1. Apr 28, 2012

### universal_101

Hello friends,

A while back I raised the similar question regarding absolute nature of Magnetic force due to a current carrying wire on a moving charge. But supposedly I was shown to be incorrect.

Since, Magnetic filed is a relativistic effect, then every magnetic force should be compatible with Principle of relativity ! right ?

But consider a simple example of a charge moving along a current carrying wire. Does it matter which one is moving, or is it the relative motion only which counts (according to Principle of relativity).

1.) current carrying wire and charge are at rest relative to each other and the charge starts moving along the wire.

2.) current carrying wire and charge are at rest relative to each other and this time it is the the current carrying wire which start moving along its length.

Now, I know, that there will be a magnetic force in scenario (1), but I think there will be NO magnetic force (of-course on the charge ) in the scenario (2).

Above preference that there will be force only when the charge will move, says Principle of relative motion does not apply to Magnetic force from a current carrying wire and a charge.

Since according to Principle of relativity, the magnetic field and therefore force should depend only on relative motion !!

And guys, don't explain the relative nature of magnetic field using the Faraday's law of induction i.e. magnet and conductor problem, since this question is about the ampere's law for magnetism.

2. Apr 28, 2012

### Staff: Mentor

The magnetic field, by itself, is not compatible with the Principle of Relativity. Neither is the electric field, by itself, compatible with the Principle of Relativity. However, the electromagnetic field (the net effect of both fields) is compatible with the Principle of Relativity. It transforms as a tensor from one inertial reference frame to another, using the Lorentz transformation.

Note that force does vary from one frame to another, in general, because it's part of a four-vector (the "four-force") which transforms according to the Lorentz transformation.

3. Apr 28, 2012

### universal_101

Well, I have No problem including all the electric fields that are associated with all the charges that constitute the scenario.

But I believe Force (or acceleration) is a absolute property i.e it does NOT depend on, from which frame observation is done. So, No matter what we have to include the two scenarios are different as long as there is Force in only one scenario.

4. Apr 28, 2012

### ZikZak

There is a force in your scenario (2). It's just not a magnetic force. It's an electric force due to the differences in length contraction between the positive and negative charges, which have different speeds, and thus different amounts of length contraction between them in the wire.

Both observers observe a force on the test charge; they merely disagree on whether it's electric or magnetic.

5. Apr 28, 2012

### universal_101

Really ? If that's the case, I don't have any further questions.

But, would there be a force on a charge if a current carrying loop passes by that charge ?

Thanks

Last edited: Apr 28, 2012
6. Apr 28, 2012

### Staff: Mentor

If there is a force in one frame then there is a force in all frames. The four-force on a particle in an EM field is given by the Lorentz force written in manifestly covariant form: $q U_{\mu} F^{\nu\mu}$ where q is the charge, U is the four-velocity, and F is the EM field tensor.

However, scenarios (1) and (2) are physically different scenarios. In (1) an accelerometer attached to the wire reads 0 and an accelerometer attached to the charge reads some non-zero value. In (2) the reverse is true. Because they are physically different scenarios relativity does NOT predict that the forces in scenario (1) will be the same as (2).

Last edited: Apr 28, 2012