Electromagnetic radiation; The Solar Spectrum; Lecture 3: Electromagnetic radiation; The Solar Spectrum; Principles of current and energy transmission 1

Decoupling Maxwell’s equations (the vacuum case) try and have equations with only E and only B Decoupling Maxwell’s equations (the vacuum case) apply the curl to Faraday’s law but Gauss’s law in the absence of charges so and Ampère’s law in the absence of currents 3-dimensional wave equations ! and similarly 2

Mathematically a wave is: The wave equation Also see Griffiths section 9.1.1 3

So electric and magnetic fields are waves with velocity = determined by experiments using electric circuits and pith balls!!!! but Conclusion: light is an electromagnetic wave Know section 9.1.1 - be able to derive the wave equation in at least one way 4

(time for one full oscillation) phase shift The most familiar form of a wave is: If phase shift is zero wave has maximum at z=0. Otherwise wave is shifted by the phase shift. k is the wave number: ν is the frequency: ω is the angular frequency (2π is one oscillation): phase amplitude wave velocity period (time for one full oscillation) 5

So in terms of angular frequency our wave is now: But sin and cos are not always easy to work with mathematically so we use Euler’s formula: and our wave is written as: with the actual wave being the real part: In electromagnetic (EM) waves the electric and magnetic fields oscillate perpendicular to the direction of motion and to each other. EM waves are transverse. 6

Visible light, radio waves, x-rays, microwaves etc Visible light, radio waves, x-rays, microwaves etc. are all EM radiation. What differs is the frequency (and thus the energy and wavelength). energy (E=hν) 7

Signal transmission: BNC cables Waveguides Analogous to acoustical waveguides e.g. doctor’s stethoscope EM waveguides usually consist of a dielectric part in which the wave travels and an outer conductor from which the wave is reflected. Examples: Signal transmission: BNC cables optical fibres (no outer conductor - light reflected off interface) in radar to bring the waves to the antenna in a microwave oven to bring the waves to the chamber 8

atmosphere blocks dangerous UV (importance of the ozone layer) 9

Energy (current) transmission When a current passes through a material energy is lost in the form of heat. This is known as Joule heating, and has the form: In order to minimise losses during transmission we must therefore minimise the current. That means raising the voltage. Remember see Joule heating Griffiths pages 289-290 Example: P = 50 W V = 10 V means I = 5 A, therefore resistance = 2 Ω V = 100 V means I = 0.5 A, therefore resistance = 200 Ω Resistance changes!! Resistance is proportional to length, so at higher voltages the same loss happens in a longer piece of cable. Most long-distance power transmission is done at 110 kV or greater 10

It’s a bad idea to run your kettle at 110 kV! So we need transformers

Transformers Voltage is changed using transformers. Transformers use Ampère’s Law and Faraday’s Law. Ampère’s Law Faraday’s Law Equation for transformers 12

At power plant transformers are used to increase the voltage. Close to point of use transformers are used to decrease voltage. Such a point is known as an electrical substation - see image below. Some transformers are also mounted close to homes 13

Examples and Problems to know: (from Griffiths 3rd edition) problems: 9.1, 9.2,9.3 and 9.4 To study sections 9.1.1 and 9.1.2 handout on Electric power transmission 14