Electromagnetic Wave and Capacitance – SS3 Physics Lesson Note (First Term)

Electromagnetic waves are transverse waves made of travelling electric and magnetic fields, and they can travel through a vacuum.

Behavioural objectives

By the end of the lesson, students should be able to:

1. explain what electromagnetic waves are and why they are transverse waves;
2. list the types of electromagnetic radiation with their wavelengths;
3. describe the sources and uses of each type of radiation;
4. name the detectors of the different radiations;
5. define capacitance and state its unit;
6. calculate charge, energy and combined capacitance in simple capacitor problems.

What are electromagnetic waves?

Electromagnetic waves are waves produced by electromagnetic vibrations, with an electrical origin, that travel in a vacuum.

• Make-up: a combination of travelling electric and magnetic forces that vary in value.
• Direction: the two forces are at right angles to each other and to the direction of travel.
• Type of wave: because of this, they are transverse waves.
• Medium: they need no material medium, so sunlight reaches the Earth through space.

What are the properties of electromagnetic waves?

All electromagnetic waves share the same basic properties, whatever their wavelength.

• Speed: they travel at 3.0 × 10⁸ m s^-1 in a vacuum.
• Wave type: they are all transverse waves.
• Energy: they carry energy from one place to another.
• Wave behaviour: they can be reflected, refracted, diffracted and made to interfere.
• Fields: they are not deflected by electric or magnetic fields.
• Difference: they differ in wavelength, frequency, source, detector and effects.

How do you calculate the wavelength of an electromagnetic wave?

The speed of an electromagnetic wave equals its frequency multiplied by its wavelength: c = fλ.

• c: speed of light, 3.0 × 10⁸ m s^-1.
• f: frequency in hertz (Hz).
• λ: wavelength in metres (m).

Worked example: a radio station transmits at 100 MHz. Find the wavelength.

1. Convert the frequency: 100 MHz = 1.0 × 10⁸ Hz.
2. Use λ = c ÷ f.
3. λ = (3.0 × 10⁸) ÷ (1.0 × 10⁸) = 3 m.

What are the types of electromagnetic radiation?

There are six main types of electromagnetic radiation: radio waves, infra-red waves, visible light, ultraviolet rays, X-rays and gamma rays.

Radio waves

• Wavelength: the longest of all the radiations.
• Source: transmitters, which carry radio signals to radio sets.
• Microwaves: the shortest radio waves, used in radar and in heating, so they are used in cooking.

Infra-red waves

• Position: just beyond the red end of the visible spectrum.
• Source: radiation from the sun or the filament of an electric lamp.
• Uses: industries use infra-red lamps to dry paint on painted items, and they are used to treat muscles.

Visible spectrum (light waves)

• Colours: red, orange, yellow, green, blue, indigo and violet, the colours of the rainbow.
• White light: formed when all these rays combine.
• Wavelength order: red has the longest wavelength and violet the shortest.
• Main source: the sun.

Ultraviolet rays

• Position: just beyond the violet end of the visible spectrum.
• Sources: the sun and mercury vapour lamps with quartz tubes.
• Effect: they make certain materials fluoresce (glow).

X-rays

• Production: fast-moving electrons strike a metal target and are slowed down.
• Medical use: destroying malignant growths and taking X-ray photographs that locate broken bones.
• Danger: large doses are harmful and can cause sterility and harmful changes in the blood.
• Industrial use: locating cracks in metal castings and flaws in pipes.
• Properties: they ionise gases and pass through substances that are opaque to white light.
• More properties: they are diffracted by crystals and unaffected by electric or magnetic fields.

Gamma rays

• Source: radioactive substances such as cobalt-60.
• Properties: like X-rays, they ionise gases and darken photographic plates.
• Penetration: their very short wavelengths give them greater penetrating power.

What are the detectors of electromagnetic radiation?

Each radiation is detected by a device or material that responds to it.

What are the uses of electromagnetic radiation?

Each type of electromagnetic radiation has its own uses in communication, medicine, industry and science.

1. Radio waves: effective communication through radio sets, television sets and walkie-talkies.
2. Infra-red rays: infra-red telescopes and signalling lamps, useful to soldiers fighting in darkness.
3. Infra-red photography: infra-red sensitive film takes clear photographs through mist and haze.
4. X-rays: inspecting broken bones in hospitals, inspecting metal castings in industry and studying crystal structure in science.
5. Gamma rays: killing cancer cells in patients, and killing bacteria in foods and hospital equipment.
6. Ultraviolet rays: ultraviolet lamps, used in experiments on the photo-electric effect.

What is capacitance?

Capacitance is the ability of a capacitor to store electric charge, equal to the charge stored per unit potential difference.

• Capacitor: a device with two conducting plates separated by an insulator called a dielectric.
• Formula: C = Q ÷ V.
• C: capacitance in farads (F).
• Q: charge stored in coulombs (C).
• V: potential difference across the plates in volts (V).
• Unit: one farad is one coulomb per volt. Smaller units are the microfarad (μF, 10^-6 F) and picofarad (pF, 10^-12 F).

What factors affect the capacitance of a parallel-plate capacitor?

• Plate area: a larger area gives a larger capacitance.
• Plate separation: a smaller distance between the plates gives a larger capacitance.
• Dielectric: a material with a higher permittivity between the plates gives a larger capacitance.
• Formula: C = εA ÷ d, where ε is the permittivity of the dielectric, A the plate area and d the separation.

How do capacitors combine?

How much energy does a charged capacitor store?

• Formulae: W = ½QV = ½CV² = Q² ÷ 2C.
• Unit: energy W is in joules (J).

Worked examples

1. A 5 μF capacitor is charged to 12 V. Charge: Q = CV = 5 × 10^-6 × 12 = 6.0 × 10^-5 C (60 μC).
2. Energy stored in the same capacitor: W = ½CV² = ½ × 5 × 10^-6 × 144 = 3.6 × 10^-4 J.
3. A 3 μF and a 6 μF capacitor in parallel: C = 3 + 6 = 9 μF.
4. The same two capacitors in series: 1/C = 1/3 + 1/6 = 1/2, so C = 2 μF.

What are the uses of capacitors?

• Tuning: selecting a station in radio and television circuits.
• Smoothing: reducing ripples in the output of power supplies.
• Storing charge: supplying a quick burst of energy, as in a camera flash.

Evaluation

1. A radio station transmits at a frequency of 1200 kHz. What is the wavelength of the radio wave? (c = 3.0 x 10⁸ m s^-1)
2. Give three similarities of electromagnetic waves. Mention two distinguishing properties of infra-red and ultraviolet rays.
3. State two properties that distinguish light waves and radio waves.
4. Mention and describe two important uses of X-rays.
5. A 4 μF capacitor is connected to a 10 V supply. Calculate the charge stored and the energy stored.

Assignment

Answer all parts.

1. State how each of these radiations can be detected: (i) X-rays, (ii) visible rays, (iii) infra-red rays.
2. Name five uses of electromagnetic radiation.
3. Two capacitors of 2 μF and 4 μF are connected in series. Find their total capacitance.