Maxwell's Equations and Electromagnetism

• Electromagnetic waves are explored, including their properties and transverse nature.
• An overview of the electromagnetic spectrum is provided, covering radio waves, microwaves, infrared, visible, ultraviolet, X-rays and gamma rays.
• It is explained that electric currents produce magnetic fields, and magnetic forces exist between current-carrying wires.
• Changing magnetic fields give rise to electric fields, and conversely, changing electric fields generate magnetic fields.
• James Clerk Maxwell proposed that a time-varying electric field can generate a magnetic field.
• Applying Ampere's circuital law to a capacitor connected to a time-varying current, Maxwell noticed an inconsistency and introduced the concept of displacement current.
• Maxwell developed a set of equations involving electric and magnetic fields, known as Maxwell's equations, which, along with the Lorentz force formula, mathematically express the basic laws of electromagnetism.
• Maxwell's equations predict the existence of electromagnetic waves, which consist of coupled, time-varying electric and magnetic fields propagating in space.
• The speed of these waves, as calculated from Maxwell's equations, is very close to the measured speed of light.
• Light is an electromagnetic wave, unifying electricity, magnetism, and light.
• Hertz experimentally demonstrated electromagnetic waves in 1885, and Marconi's work led to technological applications in communication.
• The displacement current and its consequences are discussed.
• The existance of radio waves, gamma rays, and visible light will be explained due to the displacement current Maxwell discovered.
• For logical consistency, a changing electric field must produce a magnetic field.
• Changing electric field has the important explaination the existance of radio waves, gamma rays and visible light
• The process of charging a capacitor is considered when applying Ampere's circuital law.

Displacement Current

• Maxwell showed that for logical consistency, a changing electric field must also produce a magnetic field
• It explains the existance of radio waves, gamma rays and visible light
• This field gives rise to a magnetic field along the perimeter of a circle parallel to the capacitor plates.

Maxwell's equations

• Gauss's Law for electricity
• Gauss's Law for magnetism
• Faraday's Law
• Ampere–Maxwell Law

Electromagnetic Waves

• Maxwell's theory states that accelerated charges radiate electromagnetic waves.
• Oscillating charges produce oscillating electric and magnetic fields, which regenerate each other as the wave propagates through space.
• Electromagnetic wave frequency equals the frequency of oscillation of the charge, with the energy of wave sourced from accelerated charge.
• The experimental proof came in the low frequency region (radio wave region), as in the Hertz's experiment (1887).
• Jagdish Chandra Bose succeeded in producing the first radio wave (much shorter) and observing them.
• Guglielmo Marconi succeeded in transmitting electromagnetic waves over distances of many kilometers.
• Electric and magnetic field are perpendicular to each other and to the direction of propagation with vector k (or propagation vector)
• Ex= E sin (kz-ωt)
• B = B sin (kz−ωt)
• where k is related to by the formula: k = 2π/λ
• Formula to calculate light wave is: ω= ck, where, c = 1 / √με
• νλ = c
• Formula to calculate the magnitude is: B = (E₀/c)
• The velocity of electromagnetic waves in free space or vacuum is an important fundamental constant.
• Electromagnetic waves, with wavelength ten million times that of the light waves, could be diffracted, refracted and polarised.
• he produced stationary electromagnetic waves and determined their wavelength by measuring the distance between two successive nodes
• The the total amount of electromagnetic waves is calculated as: p = U/c

Electromagnetic Spectrum

• Electromagnetic waves include visible light waves, X-rays, gamma rays, radio waves, microwaves, ultraviolet and infrared waves.
• No sharp division between one kind of wave and the next.

Radio waves

• Are are produced by the accelerated motion of charges in conducting wires, and used in radio and television.
• The AM (amplitude modulated) band is from 530 kHz to 1710 kHz.
• TV waves range from 54 MHz to 890 MHz.
• The FM (frequency modulated) radio band extends from 88 MHz to 108 MHz.
• Cellular phones use radio waves.

Microwaves

• Microwaves are produced by special vacuum tubes (called klystrons, magnetrons and Gunn diodes).
• Used for Radar systems in aircraft navigation.
• In microwave ovens, the frequency of the microwaves is selected to match the resonant frequency of water molecules.

Infrared waves

• Infrared waves are produced by hot bodies and molecules and are absorbed by the earth's surface.
• Electronic devices like semiconductor diodes emit infrared and remote switches
• Incoming visible light are radiated as infared

Visible Rays

• Detected by the the human eye
• 4 × 10¹⁴ Hz to about 7 × 10¹⁴ Hz or a wavelength range of about 700
• Different animals are sensitive to different range of wavelengths.

Ultravoilet Rays

• UV radiation is produced by special lamps and very hot bodies.
• Exposure to UV radiation induces the production of more melanin, causing tanning of the skin.
• UV radiation is absorbed by ordinary glass
• Lasik eye surgery uses UV rays
• Used in lamps to kill germs and purify water

X-Rays

• A common way to generate is to bombard a metal target by high energy electrons
• Used in medicine as a diagnostic tool and a treatment for cancer

Gamma Rays

• High frquency radiation is produced in nuclear reactions
• Also emitted by radio active nuclei
• Are used in medicine to treat certain diseases such as cancer

Explore James Clerk Maxwell's contributions to physics, including his work on electromagnetism and the nature of light. Understand how Maxwell's equations unified electricity and magnetism, and his correction to Ampere's Law. Learn about the impact of his work.