# Magnetic force on charges moving parallel with equal velocity

As we know when charges moving in an magnetic field experiences a force but what if both the body causing the field the charge under consideration moves with same velocity?....Correct me if I am wrong if we consider any external frame than it is justifiable that force acts on charges body but what if we take the charge as frame of refernce

If you have an electric charge $Q$ moving with velocity ${\bf v}$ with respect to some inertial frame through a magnetic field ${\bf B}$ created by, say, a bar magnet stationary in that frame, then the force acting on the charge is ${\bf F} = Q {\bf v} \times {\bf B}$. You appear to be asking about what happens in the rest frame of the charge? Here the charge is at rest so you might be tempted to argue "shouldn't the force be zero"? It appears that in one frame there is a force and in another there is no force.

In fact it is not strictly correct to talk about the "magnetic field" or the "electric field". Special relativity teaches us these are related and it is best to talk about the "electromagnetic field". In the rest frame of the charge there is an electric field which causes the charge to feel a force.

Is this so difficult to accept? Not if you recall that charge (which is the source of the electric field) in motion is also called current and current is the source of magnetic field. But what if you travelled with the charges? The charges are at rest so you would argue there was no magnetic field and just an electric field.

Check out the Trouton Noble experiment here.

• Sir I m just a beginner in electromagnetism so most of topic from the above experiment went over my head anyways thanks – user150960 Jun 17 '17 at 18:06

In different frame you have different field
This link or any "special relativity " book may shed light on your question.