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Consider two frames of reference S and S’ that are in relative motion and assume that a single charge q is at rest in frame S’. When an observer sees the charge in this frame, he realizes that there is an electric field existing around the charge. However, an observer in S frame sees the charge to be in motion and therefore there is an existing magnetic field along with the electric field. The magnetic field measured by the observer in S frame is created by the moving charge, which constitutes an electric current. Thus, the electric and magnetic fields are viewed differently in frames of reference that are moving relative to each other.
Consider a positive test charge q moving parallel to a current carrying wire with velocity v relative to the wire in frame S. Let us assume that the net charge in the wire is zero and the electrons in the wire also move with velocity v in a straight line. The leftward current in the wire produces a magnetic field around the wire and is directed into the page at the location of the moving test charge. So, a magnetic field away from the wire is exerted on the test charge. However, not electric force acts on the test charge since the net charge on the wire is zero when viewed in this frame.
When the same situation is viewed from the S’ frame, where the test charge is at rest, the positive charges move towards left and the electrons are at rest though the wire is still carrying current. There is no magnetic force acting here and the positive charges appear closer due to length contraction. And, the electrons are at rest. Therefore, there is a net positive charge in the wire producing an electric field pointing away from the wire towards the test charge. So the test charge experiences an electric force away from the wire. Thus, the magnetic field in the frame S is now viewed as electric field.
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