Charges and currents- a puzzle

1
Charges and currents- a puzzle

• Choice of inertial frame can affect
  interpretation of a physical situation

2
Moving Charges in reference frames
3
Moving Charges in reference frames

• 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.
• 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

4
Moving Charges in reference frames
5
Moving Charges in reference frames

• 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.

6
Moving Charges in reference frames

• 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

7
Moving Charges in reference frames

• Both observers report a force outwards from the
  wire, however the explanations are not the same.

8
Parallel moving point charges

• 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

9
Two point charges moving parallel

• 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.
• For the moving observer, the repulsive electric
  field is increased through relativistic length
  contraction. Also a magnetic field arises from
  the moving electric charge.

10
Two point charges moving parallel

• 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.

11
Maxwell and electromagnetism

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

12
Maxwells Equations
13
Maxwell and electromagnetism

• 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