Transcript Charges, currents & reference frames

Charges and
currents- a puzzle
Choice of inertial frame can affect
interpretation of a physical situation
Moving Charges in reference
frames
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
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