James Clerk Maxwell

Maxwell’s Equations 1.Gauss’ Law for E-fields –Electric charges are the beginning (source) or end (drain) of field lines 2.Gauss’s Law for B-fields –B-field lines have no beginning or end. –There is no such thing as a magnetic monopole.

Maxwell’s Equations 3. Faraday’s Law –A changing b-field induces an emf 4. Ampere-Maxwell Law –A changing e-field generates a b-field –E-fields can change even when no current is flowing

is not symmetric; it treats the magnetic field specially as the field that can create the electric field. Maxwell speculated that there was symmetry in the relationship, that an electric field could create a magnetic field. If this were true, an interesting phenomenon occurs... …E-M Radiation created by a changing current

Electromagnetic radiation A disturbance that consists of changing electric and magnetic fields that create each other through Faraday’s and Maxwell’s laws Speed depends on  and  of the medium, in a vacuum: 3x10 8 m/s

The big picture Since EM waves travel at the speed of light, light must be an EM wave If speed of EM wave depends on  and these values are constants, then the speed of light is independent of reference frame …enter Einstein and his Theory of Special Relativity (1905)

Practice problems, Ch A gaussian cylinder is 80cm long and has a radius of 12cm. Through one end is an inward magnetic flux of 25  Wb. At the other end is a uniform b-field of 1.6mT normal to the surface and directed outward. What is the net magnetic flux through the curved surface? Hint: use Gauss’s law for b-fields  Wb

More practice 27.The induced magnetic field between the plates of and 6mm from the central axis of a circular parallel-plate capacitor is 2x10 -7 T. The plates have a radius of 3mm. At what rate is the electric field between the plates changing (i.e. what is dE/dt)? Hint: There are 2 key simplifying assumptions dE/dt = 2.4x10 13