Charges and currents- a puzzle Choice of inertial frame can affect interpretation of a physical situation

Moving Charges in reference frames

O For observer at rest with respect to the external positive charge, the number of negative and positive charges balance and no net electric (electrostatic) force on the positive charge. O However, electrons in wire are moving-gives rise to an electric current to the right (conventional or positive current to right). Current creates a magnetic field – left hand rule for electron current. External charge cuts across the magnetic field and is subjected to a magnetic force from the field perpendicularly outwards. Thus the charge accelerates in response to the magnetic force. See text p. 510

Moving Charges in reference frames

O In this case, from the electrons rest frame, the observer is still at rest and the external positive charge is at rest so the magnetic field which arises should not affect the positive charge. Electrons in the wire are at rest however, the positive charges are moving to the left and thus create a magnetic field. A stationary charge in a magnetic field experiences no magnetic force.

Moving Charges in reference frames O However, the relative movement of the positive charges lead to a contraction in the spacing of the charges as perceived by the observer so the observer notices more positive charges than negative ones per unit length of the wire and the stationary positive charge experiences a net repulsive force which is electrostatic, not magnetic in origin

Moving Charges in reference frames O Both observers report a force outwards from the wire, however the explanations are not the same.

Parallel moving point charges O Consider the case where two point charges are moving at the same speed in parallel directions. Two inertial frames will be considered; one where the observer is stationary relative to the moving charges and a second where the observer is moving at a different velocity relative to the two charges. See text p. 511

Two point charges moving parallel O The observer moving with the charges sees the two positive charges repel each other and no magnetic interaction between the two i.e. the repulsive force is purely electrostatic. O For the moving observer, the repulsive electric field is increased through relativistic length contraction. Also a magnetic field arises from the moving electric charge.

Two point charges moving parallel O For the moving observer, each charge is now moving within a magnetic field created by the other charge and there is an attractive force between the charges which the observer describes as magnetic in origin. There is both an increased electrostatic repulsive force and a new magnetic attractive force compared with the stationary observer frame.

Maxwell and electromagnetism O In 1861 James Clerk Maxwell established the connection between electrostatics, electromagnetic induction, and the speed of light.

Maxwell’s Equations

Maxwell and electromagnetism O The four equations incorporate the speed of light in a vacuum. The equations conclude that if observers in different inertial frames make observations of the speed of light, then for them to agree on the laws of physics, they must observe identical values for the speed of light. This differs from and refutes the prediction made by Galilean transformations