Magnetic force in a moving coordinate system

[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?

 

[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.

 

[Orodruin]

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.

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 realized is that magnetic and electric fields, and therefore forces, transform into each other under Lorentz transformations.

 

[Tajimura]

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 realized is that magnetic and electric fields, and therefore forces, transform into each other under Lorentz transformations.

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.

 

[brianeyes88677]

Can anyone do it mathematically?

 

[Tajimura]

Can anyone do it mathematically?

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.