Electric and Magnetic Fields in Vacuum

 

 

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What are electromagnetic waves?

Electromagnetic waves are a form of energy that propagates through space as waves consisting of two perpendicular fields:

• Electric Field
• Magnetic Field

Electromagnetic waves are characterized by their ability to travel in a vacuum without the need for a physical medium, unlike mechanical waves which require a medium for propagation.

Motion in space and induction of electric fields

In space, electric fields can be induced even without the need for wires, and this is due to several physical phenomena:

1. Electromagnetic induction

When a conductor moves in a magnetic field, or when the magnetic field around a conductor changes, this generates an electromotive force (EMF) in the conductor even without connecting wires.

2. Electromagnetic waves in space

Electromagnetic energy travels through space as waves that can induce electric fields in objects placed in their path.

3. Space plasma

In space, there are vast amounts of plasma (ionized gas) that can carry electric currents and generate electric fields without the need for traditional wires.

James Maxwell

Born on June 13, 1831 in Edinburgh, Scotland. Maxwell died in Cambridge, England on November 5, 1879	James Maxwell
	Laid the theoretical foundations for the theory of the electric field in his paper on electricity and magnetism where he established the complete electromagnetic theory of light based on Michael Faraday's ideas. Which showed that oscillating charges produce waves in an electromagnetic field (1873)
Electric field resulting from a changing magnetic field Faraday's Law	Magnetic field resulting from a changing electric field Maxwell's Law

Properties of electromagnetic waves

Key properties of electromagnetic waves:

1. Travel at the speed of light (299,792 km/s in vacuum)
2. Consist of two perpendicular fields: electric and magnetic
3. Do not require a physical medium for propagation
4. Subject to reflection and refraction phenomena
5. Can be polarized

All electromagnetic waves travel
in vacuum at the same speed \[C= 3 × 10^8 m/s \] \[C=v=\frac{X}{t}=\frac{\lambda }{T}=\lambda f \]

c =v	X	t	λ	T	\[f \]
Speed of light	Distance traveled	Time	Wavelength	Period	Frequency

Example 1

The wavelength of blue light is \[λ=5×10^{-7}\; m\]
Then the frequency of the light is

Click here to show solution

Choose the correct answer

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6 × 10¹⁴ HZ

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4 × 10¹⁴ HZ

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2.5 × 10¹⁴ HZ

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5 × 10¹⁴ HZ

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Example 2

What is the frequency of an electromagnetic wave with wavelength
3.2 × 10^-7m

Click here to show solution

Choose the correct answer

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f = 6.54 × 10¹⁴HZ

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f = 4.75 × 10¹⁴HZ

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f = 8.72 × 10¹⁴HZ

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f = 9.37 × 10¹⁴HZ

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Short Quiz: Properties of Electromagnetic Waves

1. If the frequency of an electromagnetic wave is 3 × 10⁸ Hz, what is its wavelength? (speed of light = 3 × 10⁸ m/s)

a) 1 meter
b) 10 meters
c) 100 meters
d) 0.1 meter

Correct answer: a) 1 meter (Wavelength = Speed / Frequency)

2. Which of the following properties does NOT apply to electromagnetic waves?

a) They travel in vacuum
b) They need a physical medium to propagate
c) They travel at the speed of light
d) They are transverse waves

Correct answer: b) They need a physical medium to propagate (Electromagnetic waves don't need a physical medium)

3. If the wavelength of an electromagnetic wave is 500 nanometers, what is its frequency? (speed of light = 3 × 10⁸ m/s)

a) 6 × 10¹⁴ Hz
b) 6 × 10¹⁵ Hz
c) 6 × 10¹³ Hz
d) 6 × 10¹² Hz

Correct answer: a) 6 × 10¹⁴ Hz (Frequency = Speed / Wavelength)

4. What distance does an electromagnetic wave travel in 2 seconds? (speed of light = 3 × 10⁸ m/s)

a) 6 × 10⁸ meters
b) 1.5 × 10⁸ meters
c) 3 × 10⁸ meters
d) 9 × 10⁸ meters

Correct answer: a) 6 × 10⁸ meters (Distance = Speed × Time)

5. Which of the following spectra has the longest wavelength?

a) Infrared
b) Ultraviolet
c) Radio waves
d) Visible light

Correct answer: c) Radio waves (they have the longest wavelength in the electromagnetic spectrum)

6. If the frequency of an electromagnetic wave increases, what happens to its wavelength?

a) Increases
b) Decreases
c) Remains constant
d) Depends on the medium

Correct answer: b) Decreases (Frequency and wavelength are inversely proportional)

7. What is the speed of electromagnetic waves in vacuum?

a) 3 × 10⁶ m/s
b) 3 × 10⁸ m/s
c) 3 × 10⁵ m/s
d) 3 × 10¹⁰ m/s

Correct answer: b) 3 × 10⁸ m/s (This is the speed of light in vacuum)

8. What is the wavelength of an electromagnetic wave with frequency 10⁹ Hz? (speed of light = 3 × 10⁸ m/s)

a) 0.3 meter
b) 3 meters
c) 30 meters
d) 300 meters

Correct answer: a) 0.3 meter (Wavelength = Speed / Frequency)

Types of Electromagnetic Waves




The main source of electromagnetic waves is the Sun
Electromagnetic waves are divided into seven types

Infrared waves	Microwaves	Radio waves
Used in night vision cameras - remote control devices	Used in microwave ovens - radars	Used in radio and television broadcasting devices
X-rays	Ultraviolet waves	Visible light waves
Used in medical imaging- treatment of some cancer tumors	Used in water sterilization - sterilization of medical tools	Used in homes, microscopes and seeing objects
Gamma rays
Used in treatment of some cancer tumors

Short Quiz: Electromagnetic Waves

1. Which of the following types is considered an electromagnetic wave?

a. Radio waves
b. Sound waves
c. Water waves
d. All of the above

Correct answer: a. Radio waves

2. What is the relationship between the electric field and magnetic field in electromagnetic waves?

a. Parallel
b. Perpendicular
c. Opposite
d. Not related

Correct answer: b. Perpendicular

3. What is the direction of propagation of the electromagnetic wave relative to the electric and magnetic fields?

a. In the same direction as the electric field
b. In the same direction as the magnetic field
c. Perpendicular to both fields
d. No specific direction

Correct answer: c. Perpendicular to both fields

4. Which of the following is NOT an electromagnetic wave?

a. X-rays
b. Infrared
c. Ultrasonic waves
d. Gamma rays

Correct answer: c. Ultrasonic waves

5. What property differentiates electromagnetic waves from each other?

a. Speed
b. Frequency and wavelength
c. Intensity
d. Direction

Correct answer: b. Frequency and wavelength

6. Which of the following electromagnetic waves has the shortest wavelength?

a. Radio waves
b. Visible light
c. X-rays
d. Infrared

Correct answer: c. X-rays

7. How do electromagnetic waves propagate in vacuum?

a. They don't propagate in vacuum
b. At the speed of light
c. At the speed of sound
d. At speeds lower than sound

Correct answer: b. At the speed of light

8. Which of the following correctly describes the relationship between the electric field (E) and magnetic field (B) in an electromagnetic wave?

a. E = B
b. E ⊥ B
c. E ∥ B
d. E = 1/B

Correct answer: b. E ⊥ B

9. What is the source of electromagnetic waves?

a. Static electric charges
b. Accelerating electric charges
c. Constant magnetic fields
d. Earth's gravity

Correct answer: b. Accelerating electric charges

10. Which of the following electromagnetic waves is used in wireless communications?

a. Ultraviolet
b. Microwaves
c. Gamma rays
d. X-rays

Correct answer: b. Microwaves

Electromagnetic Wave Transmission
Waves are transmitted via an antenna, and the potential difference between the antenna terminals accelerates the movement of charges which in turn create a changing magnetic field due to their motion, which generates a changing electric field and so on, propagating through vacuum at a speed equal to the speed of light


A changing electric field produces a changing magnetic field which in turn produces a changing electric field and so on

Wave propagation speed in a medium
Less than the wave speed in vacuum Given by the relation \[ v=\frac{{{C}}}{{{\sqrt K }}}\] (K ) where
is the dielectric constant which varies according to the medium and equals \[ \sqrt K = n \] \[(n )\] is the refractive index of the medium

Example 3

If the dielectric constant of glass is \[ K=2.28 \]
Then the speed of light in glass equals

Click here to show solution

Choose the correct answer

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1.3 × 10⁸ m/s

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2.5 × 10⁸ m/s

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1.5 × 10⁸ m/s

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2 × 10⁸ m/s

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Short Quiz on Electromagnetic Wave Transmission

1. How do electromagnetic waves propagate in vacuum?

a. Through movement of material particles

b. Through changing electric and magnetic fields

c. Through sound waves only

d. Through direct electric current

Correct answer: b. Through changing electric and magnetic fields

2. What causes the generation of magnetic field in an antenna?

a. Accelerating charge movement

b. Heat generated by the antenna

c. Atmospheric pressure

d. Earth's gravitational field

Correct answer: a. Accelerating charge movement

3. What is the propagation speed of electromagnetic waves in vacuum?

a. Depends on wave frequency

b. Equals the speed of light

c. Less than speed of sound

d. Undefined

Correct answer: b. Equals the speed of light

4. What is the relationship between wave speed in a medium and its speed in vacuum?

a. Greater in the medium

b. Equal in both cases

c. Less in the medium

d. No relationship between them

Correct answer: c. Less in the medium

5. What factor affects the speed of electromagnetic waves in a medium?

a. Dielectric constant (K)

b. Medium color

c. Medium mass

d. Medium size

Correct answer: a. Dielectric constant (K)

6. What is the relationship between refractive index (n) and dielectric constant (K)?

a. n = K

b. n = √K

c. n = K²

d. No relationship between them

Correct answer: b. n = √K

7. What happens to the speed of electromagnetic waves when they move from vacuum to a medium?

a. Increases

b. Decreases

c. Remains the same

d. Becomes zero

Correct answer: b. Decreases

8. What is the role of the antenna in electromagnetic wave transmission?

a. Convert electrical energy to electromagnetic waves

b. Store electromagnetic waves

c. Filter unwanted waves

d. Increase wave speed

Correct answer: a. Convert electrical energy to electromagnetic waves

9. What generates the changing electric field in electromagnetic wave transmission?

a. Changing magnetic field

b. Earth's gravity

c. Medium temperature

d. Atmospheric pressure

Correct answer: a. Changing magnetic field

10. How does the speed of electromagnetic waves change with increasing dielectric constant of the medium?

a. Increases

b. Decreases

c. Remains constant

d. Becomes undefined

Correct answer: b. Decreases

Electromagnetic Wave Production

How do radio stations work?

Radio broadcasting process

Audio signal ← modulation ← carrier wave ← transmission ← reception ← demodulation ← sound

Carrier Waves

Each radio station has its own carrier wave at a specific frequency in the electromagnetic spectrum. In the United Arab Emirates, specific frequencies are allocated to each station.

Transmitter Components

1. Oscillator

Creates the basic carrier wave at a specific frequency (up to 400 MHz).

Consists of a coil and capacitor connected in series.

2. Modulator

Uses the audio signal (music/speech) to modify characteristics of the carrier wave:

• Amplitude Modulation (AM)
• Frequency Modulation (FM)

3. Amplifier

Strengthens the modulated signal before transmitting it via the antenna.

How does the LC oscillator work?

Complete oscillation cycle:

1. The capacitor is charged with electrical voltage, creating an electric field and storing charges
2. When voltage is removed, the capacitor discharges through the coil
3. The current in the coil creates a changing magnetic field
4. The changing magnetic field induces an electromotive force that recharges the capacitor in the opposite direction
5. The process repeats in the opposite direction

Thus creating a changing electric field and changing magnetic field at a specific frequency

Resonance frequency equation

\[f = \frac {1 } {2π \sqrt {LC}}\]

Where:
f = Frequency (Hz)
L = Inductance of the coil (Henry)
C = Capacitance of the capacitor (Farad)

How is this converted to sound?

In your radio:

1. The antenna receives electromagnetic waves
2. The circuit is tuned to the carrier frequency of the desired station
3. The audio signal is separated from the carrier wave (demodulation)
4. The audio signal is amplified and directed to speakers

Stable Oscillations in Electrical Circuits

Similarity between pendulum and electrical circuit

Just as friction causes a pendulum to stop if left alone, oscillations in a coil and capacitor will dampen over time due to energy being radiated as electromagnetic waves and due to circuit resistance.

By adding energy to both systems, the oscillations continue. Gentle pushes to the pendulum at the right times will keep it swinging.

Resonance phenomenon

The amplitude of the pendulum's swing reaches its maximum when the frequency of the pushes matches the frequency of the swing and are in phase. This is the resonance condition you read about in a previous unit.

Just as gentle pushes help maintain the pendulum's motion, voltage differences applied to a coil and capacitor circuit at the appropriate frequency maintain the oscillations.

Role of transformer in maintaining oscillations

Among the methods to maintain oscillations in the circuit is adding a second coil to create a transformer. The transformer works to:

• Transfer energy from an external source to the resonant circuit
• Maintain frequency proportional to the circuit's resonant frequency
• Compensate for energy lost due to resistance and electromagnetic radiation

When an oscillating current passes through the first coil (L1), it generates a changing magnetic field that affects the second coil (L2) which is connected to a power source. This electromagnetic interaction between the two coils maintains the oscillations in the resonant circuit (L1 and C) by compensating for lost energy.

Frequencies in Resonant Cavity

The frequency generated by a coil and capacitor circuit can be increased by:

• Reducing the coil's ability to store magnetic energy
• Decreasing the capacitor's electrical capacitance

Limits of coils and capacitors

Coils and capacitors become ineffective at frequencies exceeding 400 MHz.

Microwave waves and resonant cavity

Microwave waves ranging between 0.4 GHz to 100 GHz are generated using a resonant cavity, which is a rectangular metal box that acts as both a coil and capacitor simultaneously.

Frequency control

The box size controls the oscillation frequency. Note that in microwave ovens, the oven size itself doesn't affect the wave frequency; only the size of the resonant cavity in the oven affects the frequency.

Very high frequencies

To produce waves with frequencies exceeding 100 GHz, the resonant cavity size must be reduced to molecular size.

Infrared and light

Infrared, for example, is generated by vibration of nuclei within molecules. High frequency light waves and ultraviolet waves and X-rays are caused by electron movement within atoms.

Gamma waves

Gamma waves, which have the highest frequency, are generated by acceleration of charges in atomic nuclei.

Summary:

1. Frequency increases by reducing component size
2. Resonant cavity replaces coil and capacitor at high frequencies
3. Frequency is inversely proportional to cavity size
4. Higher frequencies require smaller structures (molecular and atomic)

Piezoelectricity and electromagnetic wave generation

There are multiple methods to generate oscillating voltage differences for transmitters. One of these methods relies on the piezoelectric phenomenon in some crystals like quartz.

Piezoelectricity in quartz crystals

Quartz crystals deform when exposed to electrical voltage, a property known as piezoelectricity. When AC voltage is applied to a piece of quartz crystal, continuous oscillations are generated.

Quartz crystal used to generate oscillations

Principle of piezoelectric crystals

Just as a metal piece vibrates at a specific frequency when bent and released, so do quartz crystals. The thinner the crystal, the higher its vibration frequency.

The piezoelectric property in crystals generates an electromotive force when the crystal is deformed. This electromotive force results from the crystal's vibration frequency, and thus can be amplified and returned to the crystal to keep it vibrating.

Practical applications

Due to their nearly constant vibration frequencies, quartz crystals are widely used to create electromagnetic waves in:

• Cell phones
• Televisions
• Cordless phones
• Computers
• WiFi wireless routers

Electromagnetic Wave Reception System

Antenna Wire

How an antenna works

The antenna converts electromagnetic energy into electric currents that can be processed:

1. The electromagnetic wave reaches the antenna wire
2. The electric and magnetic fields in the wave cause electron movement in the wire
3. This movement converts to alternating current (AC)
4. This current transfers to the receiver for processing

Relationship between antenna length and wavelength

There is a fundamental relationship between antenna length and target wavelength:

Optimal antenna length = λ/2 or λ/4

Where λ is the electromagnetic wavelength.

For an antenna to be effective at receiving a specific wave, its length must be proportional to that wave's length. Typically, the most efficient antennas are those that are half the wavelength (λ/2) or quarter wavelength (λ/4) long.

Satellite reception dishes

Dish orientation and adjustment

The satellite dish must be precisely directed toward the satellite to be received:

1. Horizontal angle: Dish direction relative to magnetic north
2. Vertical angle: Dish tilt relative to horizon
3. Polarization angle: Feed horn rotation angle around its axis

Wave reception method

Satellite reception dishes work on the focal point principle:

1. The large dish receives weak electromagnetic waves from space
2. The parabolic surface reflects waves toward the focal point where the feed horn is located
3. The feed horn converts high frequency waves to lower frequencies that can be transmitted via cable
4. The signal travels via cable to the receiver for processing

Wave Reception Simulation

Electromagnetic Wave Reception System

Antenna Wire

Reception Antenna Control

Antenna length: Antenna angle:

Received signal strength: Medium

Satellite Dish

Satellite Dish Control

Dish angle: Focus adjustment:

Satellite signal quality: Good

Information about electromagnetic wave reception

Reception systems convert electromagnetic waves into electrical signals that can be processed.

The antenna (wire antenna) receives radio waves, while satellite dishes are used to receive high frequency satellite signals.

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