4) A plane wave of wavelength 1.2 m propagates in the z-direction. The electric field points in the y-direction and has an amplitude of 3.0 V/m. Write an expression for the magnetic field, including its amplitude. Assume that the electric field is at its maximum at z=0, t=0.

(the space variable is z because the wave is moving in the z direction)

We must have pointing in the direction, so must point in the direction.

The wavelength and frequency are the same for the electric and magnetic fields.

So

) A thin layer of a transparent material with an index of refraction of 1.30 is used as a nonreflective coating on the surface of glass with an index of refraction of 1.50. What should the thickness of the material be for it to be nonreflecting for light of wavelength 600 nm (in a vacuum)? Please give details of your reasoning.

Both reflections occur against a surface of higher index of refraction, so there is a phase shift at each reflection. The phase shifts cancel each other out, so if we want the emerging rays to be out of phase, we must have

) A Teflon rod of radius 4.0 cm and height 20.0 cm is being charged uniformly over its surface. How much charge can the rod hold before the surrounding air breaks down electrically, which happens when the electric field in air is N/C? Ignore the likelihood of breakdown at the sharp edges.

Choose a Gaussian surface just outside the cylinder. Then

If E is the field at which there's a breakdown, then