# What would happen to a charge in uniform magetic field when observed from a moving reference frame?

Suppose there is a uniform magnetic field everywhere in the space in -z axis direction. And suppose there is a particle at rest with respect to our reference-frame. The arrangement is shown in the figure : Now, suppose our reference frames starts moving to the right with a constant velocity. The charged particle would appear to be moving to the left with the same velocity. Now, will there be any magnetic force acting the the charged particle ?

## 1 Answer

Yes, a magnetic force will appear, for the frame independent quantity is not the magnetic, but the Lorentz force. An electric field will appear as a consequence, so that the particle is subject to the same force in both frames.

• so, the particle will still only move because of the relative motion, because other forces (magnetic and electric) will cancel each other ? – 0xVikas Apr 12 '18 at 14:08
• Yes, no acceleration will appear. – Othin Apr 12 '18 at 14:19
• Thank you, But can you give me much more details ? Like mathematical description ? – 0xVikas Apr 12 '18 at 15:59
• The math comes down to the transformation of the electromagnetic field components under a Lorentz transformation. When you change between inertial frames, those components change according to certain formulas. Letting the velocity be in the x-direction, the formulas can be found in table 26.2 from the link bellow (I would write them here but I'm typing from my phone, in which I find them hard to type) Noting that all components except Bz were zero, try to use them to calculate the Lorentz force. feynmanlectures.caltech.edu/II_26.html – Othin Apr 12 '18 at 20:48
• Thank you for clarifying my doubts ! It was really helpful. – 0xVikas Apr 13 '18 at 9:43