1. James Clerk Maxwell

2. 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.

3. 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

4. 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

5. 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

6. 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)

7. Practice problems, Ch. 32 3.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. -47.4  Wb

8. 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