# Does protons moving parallel to each other exert magnetics force

If two protons are moving parallel to each other in same direction with equal velocities then do they exert magnetic force on each other.? As protons are moving they should produce magnetic field and there should be some magnetic force + electric force on each of them. But if look from their refrence frame then both the protons are at rest and hence there will be no magnetic force (as magnetic field is created by a moving charge), only electric force on each of them. How can this be possible that force(magnetic force) on a particle becomes different on changing the reference frame even though the reference frames are non accelerating with respect to each other?

## 1 Answer

Whether they exert both electric and magnetic forces on each other, or only electric forces, depends on which reference frame you use. Electric and magnetic fields transform into each other under changes of reference frame. This is why we talk about the electromagnetic field as if it were one unified tensor field $$\mathbf{F}$$ rather than two different vector fields $$\vec{E}$$ and $$\vec{B}$$.

• Then electric force also depend on referece frame ? – Param_1729 Jul 11 at 4:35
• Yes, electric field and electric force depend on the reference frame. – G. Smith Jul 11 at 4:36
• MathJax gurus, how can I write a tensor using a bold san-serif font? – G. Smith Jul 11 at 4:45
• Is there some intuition or is it that that i am not understanding it as it is taught to me as seperate chapters – Param_1729 Jul 11 at 4:48
• Your example provides the intuition. A magnetic field is produced by moving charge. Whether something is moving or not, and how fast, depends on the reference frame used to observe it. So obviously magnetic fields must be frame-dependent. Given how Maxwell’s equations link electric and magnetic fields, it should not he surprising that electric fields are also frame-dependent. – G. Smith Jul 11 at 4:51