Electro Magnetism and Relatively

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Magnetic Force on the charged particles is given by

$\mathbf{F}=q(\mathbf{v}\times \mathbf{B})$

Where v is the velocity which is frame dependent.So different observer will calculate different Magnetic Force

Or

A charge at rest produces no magnetic field but a moving charge produces a magnetic field. Again moving charge depends on frame of refrence

Let say A charge q is placed on the trolley moving on the rail. A person on the earth will observe magnetic field will be produced as the charge is moving.While a person on trolley applying law of electrdynamics will predict the magnetic field to be zero

So it may appear, electro dynamic theory assumed the existence of unique stationary refrence frame with respect to all velocities need to be measured

Let us take one more example, A wire loop is placed on the trolley and passes it through the poles of the gaint magnet.

Now as loop moves through the magnetic field,the charges experience motional emf and according to flux rule

$e=-\frac{d\phi}{dt}$

This emf is generated becuase of the magnetic forces on the charges which are moving along with the trolley

Now for the person sitting on the trolley,the charges are at rest,So he will predict no magnetic force on the charges as per electrodynamics theory.But he will observed that magnet is moving with respect to him and magnetic field will change in the loop due to magnet and We know that changing magnetic field induced electric field in the loop and resulting electric force would generate emf given by

$e=-\frac{d\phi}{dt}$

So both the observer will get the same answer but through different interpretation of the processes. One through magnetic force and other through electric force.

So I would like to make following points

1) Electric and magnetic force are frame dependent

2) That is to say, whether you observe an electric field, a magnetic field, or a “mixture” of the two is dependent on your frame of reference, i.e., the electric and magnetic fields are really just two sides of the same coin. Regardless of whether you see the electric field or the magnetic doing the job, i.e. regardles of your frame of reference, you will still observe the same physical results