Magnetic force in a moving coordinate system

1. Apr 3, 2015

brianeyes88677

Consider a line charge with charge density λ and a electric charge q. A coordinate system moving at velocity v ,it will see the line charge as a current ,and the electric charge(which is also moving seen from the moving coordinate system) will feels magnetic force. Why does this happens?

2. Apr 3, 2015

Tajimura

[strike]In a moving reference frame the line charge and the point charge are not moving relative to each other, so the charge will not "feel" any magnetic field.[/strike]
Disregard that, it's not correct.

Last edited by a moderator: Apr 3, 2015
3. Apr 3, 2015

Orodruin

Staff Emeritus
This is irrelevant, the charge is moving and there is a magnetic field, so the charge will be subjected to a magnetic force. What needs to be realised is that magnetic and electric fields, and therefore forces, transform into each other under Lorentz transformations.

4. Apr 3, 2015

Tajimura

Yup, you are right. It just rained down on me after I send the answer and left the forum, that relative speed of charges bears no importance here. Magnetic force is just a relativistic effect of changing a reference frame, and though moving observer is observing additional magnetic force, electric force observed by him is less than the electric force observed by stationary observer, so full force is just the same in both cases.

5. Apr 3, 2015

brianeyes88677

Can anyone do it mathematically?

6. Apr 3, 2015

Tajimura

Just insert linear change field into Lorentz transformations with burst v and see how the field get transformed into linear combination of electric and magnetic fields.