MODULE 7 IQ1 Flashcards
maxwell’s 4 equations
- div D = ρ
- div B = 0
- curl E = -dB/dt
- curl H = dD/dt + J
1st equation: guass’ law (electricity)
- electric field lines leave positive charges and terminate on negative charges
- the strength of an electric field depends on the magnitude of the point charge producing it
2nd equation: guass’ law (magnetism)
- describes the concept of magnetic field lines being enclosed and continuous at all times
- thus, magnetic monopoles do not exist
3rd equation: faraday’s law
- a changing magnetic field induces an electromotive force (EMF) and hence an electric field.
- this EMF always opposes the initial change
4th equation: ampere-maxwell law
- B fields are able to be generated in 2 different ways:
1. current/moving charges –> use right hand grip rule
2. changing electric fields
maxwell’s theory of electromagnetism
- 3rd equation: Lenz’s law recognises that a changing B-field creates an E-field
- 4th equation: Maxwell’s law recognises that a changing E-field creates a B-field
- wave requires no medium as it is self-propagating: an electromagnetic wave
- produced by oscillating charges (4th law)
- creates B-field –> change in B-field –> change in E-field (3rd law) –> cycle continues
structure of electromagnetic waves
- self-propagating
- composed of 2 sinusoidal waves which are in-phase, perpendicular to each other, and are an electric field and magnetic field
electromagnetic waves composition
- always travels at the speed of light ‘c’
- travels slower in denser mediums
- there is no restriction on frequency –> therefore, he predicted that the whole spectrum of wavelengths of EMR should exist
- any accelerating charge emits EMR
hertz experiment to confirm maxwell’s theory
alternating current (AC) circuit resonating at a known frequency connected to a loop of wire. high voltages induced across the gap in the loop resulted in visible sparks, providing tangible evidence of the current in the circuit and contributing to the generation of EM waves. the frequency of the AC was synchronised with the oscillating electric and magnetic fields, which in turn matched the frequency of the EM wave produced.
hertz experiment calculation
2 sinusoidal waves –> nodes –> carrying no energy –> spark in receiver –> manually measured the distance between the 2 closest nodes λ/2 & multiplied by 2 to find wavelength. plugged into v=fλ
historical methods of measuring the speed of light
fizeau, foucault
fizeau experiment
placing a reflective mirror at a distance from the light source, fizeau observed the return of light to an observer positioned adjacent to the source. by adjusting the angular velocity (w=Δθ/Δt) of the spinning toothed wheel, fizeau ensured that the returning light either passed through or was blocked by the gaps between the teeth, depending on the wheel’s rotation speed. by controlling the speed and knowing the distance between the wheel and the mirror, fizeau successfully calculated the speed of light to be 313 300km/sec
foucault experiment
beam of light was directed towards a distant rotating mirror, which reflected it onto a nearby fixed mirror. the light was redirected back to the rotating mirror. as the rotating mirror constantly turned, the angle at which the light initially struck it differed from the angle upon its return from the fixed mirror. by measuring the angle displaced by the mirror and its angular velocity, foucault calculated the time taken for the light to travel which was 298 000 000m/s
contemporary methods of measuring the speed of light
rosa and dorsey (1907)
- deduced the value by determining the electric and magnetic properties of the vacuum.
- relied on maxwell’s theoretical framework to establish the speed of light using the vacuum’s electric permittivity ε and magnetic permeability µ
spectroscopy definition
study of absorption and emission of light –> the observation of spectra
- spectra tells us what wavelengths are present (colour) and intensity (brightness of particular wavelengths)
emission spectra
- long dark rectangular strips with discrete bright coloured bands
- produced by hot gases of low density –> bright coloured bands represent specific discrete wavelengths that are emitted by the gas atoms
- every element will have different values for their energy levels, resulting in different energy photons being produced
emission spectra description
heat = increase in kinetic energy –> form of energy that allows electrons to jump energy levels
bohr’s model of the atom
states that electrons in an atom only orbit in specific stationary states which have a specific energy level
- if an electron wants to jump into a higher energy state, it must receive energy equivalent to the difference in energy between its original state and the one it will jump to
- if an electron drops to a lower energy level, it will release energy such that it will produce EMR following E=hf
continuous spectra description
continuous wavelength range of light
- directly insinuates a continuous frequency of lgiht, as the speed of light is a constant value
- produced by a hot, glowing solids, liquids or high-pressure gas
absorption spectra description
- the missing spectral lines will correspond to the same element’s emission spectra (whatever photon can be emitted can also be absorbed, as it is the same electron transition just in reverse)
stellar characteristics in stellar spectra
surface temperature, rotational and translational velocity, density, chemical composition
how to determine surface temperature in stellar spectra
peak wavelength of stellar spectrum follows Wien’s displacement law, λ(max)=b/T, where λ(max) is the peak wavelength, T is the surface temperature and b is Wien’s displacement constant.
how to determine rotational and translational velocity in stellar spectra
the doppler effect causes the spectral lines of a star to shift depending on its velocity relative to the observer. a blueshift indicates the star is moving towards us, while a redshift indicates it is moving away.
- degree of line broadening can also be used to estimate the star’s rotationa’ velocity
how to determine density in stellar spectra
pressure broadening of spectral lines can be indicative of a star’s atmospheric density
- higher density leads to more collisions between particles which in turn broadens the spectral lines
how to determine chemical composition in stellar spectra
each element absorbs and emits light at specific wavelengths. by analysing the absorption lines in a star’s spectrum, the presence and abundance of elements can be identified, revealing the star’s chemical composition
