Physics 213General Physics

Lecture 14

2

Last Meeting: Electric Generators, Alternating Current

Today: Electromagnetic Waves, Maxwell’s Equations

Electromagnetic Properties, Summary(1) Electric field Sources

(2) No magnetic field sources

(3) Changing magnetic field produces an electric field (Faraday’s Law)

(4) Moving charge (current) produces magnetic fields.

2041rQ

E

trE B

2

CIrB 02

4

Changing E field produces B field

0E

dit

t

IrB EC 002

CIrB 02

A changing E field produces a B field.

Can be viewed as formed from a “displacement current”.

EM Waves by an Antenna

Two rods are connected to an ac source, charges oscillate between the rods (a)

As oscillations continue, the rods become less charged, the field near the charges decreases and the field produced at t = 0 moves away from the rod (b)

The charges and field reverse (c) The oscillations continue (d)

EM Waves by an Antenna, B field Because the oscillating

charges in the rod produce a current, there is also a magnetic field generated

As the current changes, the magnetic field spreads out from the antenna

The magnetic field is perpendicular to the electric field

Electromagnetic Waves Can Propagate in Free Space A changing magnetic field produces an

electric field A changing electric field produces a

magnetic field These fields are in phase

At any point, both fields reach their maximum value at the same time

Electromagnetic Waves are Transverse Waves

The and fields are perpendicular to each other

Both fields are perpendicular to the direction of motion Therefore, em waves

are transverse waves

E

B

Properties of EM Waves

Electromagnetic waves are transverse waves Electromagnetic waves travel at the speed of

light (3x108 m/s)

Because EM waves travel at a speed that is precisely the speed of light, light is an electromagnetic wave

1

o o

c

Properties of EM Waves, 2

The ratio of the electric field to the magnetic field is equal to the speed of light

Electromagnetic waves carry energy as they travel through space, and this energy can be transferred to objects placed in their path

Ec

B

Properties of EM Waves, 3

o o o

Average power per unit area

E B E c BI

c

2 2

max max max max

2 2 2

The Spectrum of EM Waves

Forms of electromagnetic waves exist that are distinguished by their frequencies and wavelengthsc = ƒλ

Wavelengths for visible light range from 400 nm to 700 nm

There is no sharp division between one kind of EM wave and the next

The EMSpectrum

Note the overlap between types of waves

Visible light is a small portion of the spectrum

Types are distinguished by frequency or wavelength

14

15

Right-Hand Rule Review Sheet

In an RLC circuit, the maximum current is 1 amp. What is the average current?

17

1. 21/2 A

2. (1/21/2) A

3. (1/2) A

4. Non of the above

An AC voltage source, with a peak output of 200 V, is connected to a 50- resistor. What is the effective (or rms) current in the circuit?

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1. 2.8 A

2. 4.0 A

3. 5.6 A

4. 2.0 A

A 100 Hz AC voltage source, with a peak output of 170 V, is connected to an inductor. If the rms current through the inductor is 1 A, what is the value of the inductor?

19

1. 1.9 H

2. 190 mH

3. 19 mH

4. 1.9 mH

In a circuit made up of inductor L, resistance R, ammeter, battery and switch in series, the current is greatest at which of the following times, as measured after the switch is closed?

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1. Zero

2. One time constant

3. At time t=L/R

4. Ten time constants