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As the first half wavelength of the approaching wavefront reaches the atom shown, the E -field. E. c. B. 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.

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Presentation Transcript
slide1

As the first half

wavelength of the

approaching wavefront

reaches the atom

shown, the E-field

E

c

B

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.

slide2

As the electrons move down under the influence of the E-field, the oncoming B-field in the same half wavelength

pushes those electrons

E

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.

c

B

slide3

As the protons move up under the influence of the E-field, the oncoming B-field in the same half wavelength

pushes those protons

E

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.

c

B

wave intensity

Intensity = power / area

r2

r1

Wave Intensity

Intensity: Energy transported per unit area per second

Power transported per unit area.

As the wave moves outward, energy gets spread out over a wider and wider area, so the wave intensity gets smaller.

Surface area of a sphere = 4R2

What is the intensity of EM waves?

slide5

Recall

1

2

1

2

1

2

1

2

Energy stored in the electric field within a capacitor: CV2

withC = oA/d and V=Ed

so PEEfield = (oA/d)(Ed)2 = o(Ad)E2

1

2

1

2

uE= oE2

Similarly

Energy stored in the magnetic field of a solenoid: LI2

whereL = NBA/Iand B=moI(N/)

1

2

so PEBfield = (NBA/I)I2 = NBA(B/moN)2

1

2mo

PEBfield = (A)B2

uB= B2

We say the “energy density”

within the magnetic field is

1

2mo

slide6

A

A

cDt

During a time Dt, an electromagnetic wave will

deliver energy to/through any surface A it

illuminates:

AcDt(uB+ uB )

slide7

Since E (B) is continuously induced/created by B (E) expect

EB

and since the total energy is continuously exchanged

betweenE and B

we expect (for EM waves), at every point in space:

uB= uB

slide8
The rate at which electromagnetic energy is being transferred by an EM wave through any given area is:

Units:

W / m2

or

slide9

Compared to wave 1, the power

transported by wave 2 is about

1) half

2) the same

3) double

4) quadruple

slide10
The rate at which electromagnetic energy is being transferred by an EM wave at any given moment through any given area is:

instantaneous

field values!

Remember!

E and B fields fluctuate

with time!

slide11

You should recall that the

time average of E(t) is zero.

1

4

1

2

1

2

1

2

Eo2sin

2

Eo

Eosin

Eo

2

Eosin

What is the average E2(t)?

  • 0
  • Eo
  • Eo
  • 4) Eo
  • ( Eo)2
  • Eo2
average intensity and rms values

0

0

< Emax2 / oc

< Emax

Emax2 / oc

Emax

Average Intensity and RMS values

Energy

delivered

E field

Because intensity is constantly changing, we work with the average intensity

Average over one full wavelength. Since E varies sinusoidally,

(E2)avg = ???(Emax2).

(1/2)

average intensity and rms values1

0

0

0

0

< Emax2 / oc

< Emax2 / oc

< Emax

< Emax

Emax2 / oc

Emax2 / oc

Emax

Emax

E2

oc

1

2

Sav =

1

2

1

2

Erms = Emax

Brms = Bmax

Average Intensity and RMS values

Energy

delivered

E field

Because intensity is constantly changing, we work with the average intensity

Average over one wavelength. Because E is a sine wave, the average is 1/2.

To get average, you have two choices:

1. Remember the factor of1/2

2. Usermsvalues for E and B and use standard equation: S = E2/oc

Sav = Erms2/oc

slide14

Charge vibrates

linearly along the

direction illustrated.

This oscillating

dipole emits

transverse waves

preferentially

in what direction?

1

2

3

Waves are transmitted

equally in all directions

4

5

slide15

E

c

B

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

slide16

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.

Intensity is proportional to the square of the E or B fields.

4) quadruple

If the amplitude of the fields doubles, it must mean 4x as much energy.

  • Eo2

Just look at the graph of E2 to judge where the average of those oscillations are.

4

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.