As the first half wavelength of the approaching wavefront reaches the atom shown, the E -field 1) pushes the electron cloud up, the nucleus down. 2) pushes the electron cloud left, the nucleus right. 3) pushes the electron cloud right, the nucleus left. 4) pushes the electron cloud down, the nucleus up.

As the electrons move down under the influence of the E -field, the oncoming B - field in the same half wavelength pushes those electrons 1) toward the right of the screen. 2) toward the left of the screen. 3) up. 4) down. 5) forward, in the direction of c. 6) backward, into the screen.

As the protons move up under the influence of the E -field, the oncoming B - field in the same half wavelength pushes those protons 1) toward the right of the screen. 2) toward the left of the screen. 3) up. 4) down. 5) forward, in the direction of c. 6) backward, into the screen.

Wave Intensity Intensity = power / area What is the intensity of EM waves? As the wave moves outward, energy gets spread out over a wider and wider area, so the wave intensity gets smaller. Intensity:Energy transported per unit area per second Power transported per unit area. Surface area of a sphere = 4  R 2 r1r1 r2r2

Recall Energy stored in the electric field within a capacitor: CV with C =  o A/d and V=Ed so PE Efield = (  o A/d)(Ed) 2 =  o (Ad)E u E =  o E Similarly Energy stored in the magnetic field of a solenoid: LI where L = NBA/ I and B=  o I (N/ ) so PE Bfield = (NBA/ I ) I 2 = NBA(B /  o N) We say the “energy density” within the magnetic field is u B = B 2 12o12o PE Bfield = (A )B 2 12o12o

ctct During a time  t, an electromagnetic wave will deliver energy to/through any surface A it illuminates: Ac  t ( u B + u B )

Since E ( B ) is continuously induced/created by B ( E ) expect E  B and since the total energy is continuously exchanged between E and B we expect (for EM waves), at every point in space: u B = u B

The rate at which electromagnetic energy is being transferred by an EM wave through any given area is: Units: W / m 2 or

Compared to wave 1, the power transported by wave 2 is about 1) half 2) the same 3) double 4) quadruple

The rate at which electromagnetic energy is being transferred by an EM wave at any given moment through any given area is: Remember! E and B fields fluctuate with time! instantaneous field values!

EoEo EoEo 2 E o sin  2 You should recall that the time average of E(t) is zero. What is the average E 2 (t)? 1) 0 2) E o 3) E o ) E o 5) ( E o ) 2 6) E o E o 2 sin 

Average Intensity and RMS values Average over one full wavelength. Since E varies sinusoidally, (E 2 ) avg = ??? (E max 2 ). E field Energy delivered Because intensity is constantly changing, we work with the average intensity 00 < E max 2 /  o c < E max E max 2 /  o c E max (1/2)

Average Intensity and RMS values Average over one wavelength. Because E is a sine wave, the average is 1/2. S av = E2ocE2oc 1212 E field Energy delivered 00 Because intensity is constantly changing, we work with the average intensity E rms = E max 1 2 B rms = B max 1 2 < E max 2 /  o c < E max E max 2 /  o c E max 00 < E max 2 /  o c < E max E max 2 /  o c E max To get average, you have two choices: 1.Remember the factor of 1/2 2.Use rms values for E and B and use standard equation:S= E 2 /  o c S av = E rms 2 /  o c

Charge vibrates linearly along the direction illustrated. This oscillating dipole emits transverse waves preferentially in what direction? Waves are transmitted equally in all directions

The magnetron of a microwave horn generates a horizontally varying B-field and oscillating vertical E-field. We found which of the aluminum gratings below let the microwaves pass? 1 2

4) pushes the electron cloud down, the nucleus up. E-field up, so positive charges are pushed up, negative charges down! 5) forward, in the direction of c. B-field left, with electrons (use left hand!) moving down. 5) forward, in the direction of c. B-field still left, but use right hand now for The positive protons moving up. 4) quadruple Intensity is proportional to the square of the E or B fields. If the amplitude of the fields doubles, it must mean 4x as much energy. 5) E o Just look at the graph of E 2 to judge where the average of those oscillations are. Most of the energy is transmitted perpendicular to the direction the charge vibrates.. 2 The vertical slats act as antenna absorbing energy from the microwaves as current surges up and down. The horizontal slats are ineffective current paths, and let the microwave energy pass, unused.