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98 Cards in this Set
- Front
- Back
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writing vectors |
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ways to draw vectors |
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stokes theorum |
vector stacks don't match up discontinuities are sheafs |
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gauss' theorum |
sheaf field where one point is stronger so creates discontinuities |
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grad |
scalar to vector |
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div |
vector to scalar |
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curl |
vector to vector |
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helmhotz theorum |
a field completely determined by divergence, curl and boundary conditions |
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laplacian |
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splitting curls and divs |
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types of vector in Cross product |
2 arrows make a thumbtack 2 stacks make a sheaf |
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levi civita symbol |
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kronecker delta |
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equations using levi civita function is and kronecker function |
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unit vectors |
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maxwell equations |
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deriving 1st maxwell equation |
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deriving 2nd maxwell equation |
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deriving 3rd maxwell equation |
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deriving 4th maxwell. equation |
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corrected 4th maxwell equation |
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lorentz force |
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original potentials |
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New potentials |
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proof of new potentials |
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Hamiltons equations of motion |
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poisson equation |
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method of imagining |
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laplace in 1D |
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laplace in 3D |
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laplace in 2D |
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First uniqueness theorum |
in volume V with a surface S has a unique solution when ø is on surface S |
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second uniqueness theorum |
electric field in volume V is specified by the total charge on each conductor surrounding V and the charge density Inside V |
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Qml and scalar potential |
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monopoles |
Qml =0 when L ≠0 |
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dipoles |
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Mlm and vector potential |
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when to calculate Mlm |
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Mlm for loop of wire |
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maxwell equations in a vacuum |
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dispersion relation |
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what happenes if a wave packet moves in time |
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linear polarisation |
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circular polarisation |
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poynting vector |
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poynting theorum and meaning of each term |
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maxwell tensor Tij |
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lorentz force in terms of maxwell. tensor |
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creating radiation |
accelerating charge |
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retarded time |
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retarded dipole moment |
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retarded scalar potential |
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retarded vector potential in terms of poynting vector |
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retarded I in vector potential |
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relation between Pr and Ir |
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retarded vector field |
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calculating E field using retarded potentials |
E field must be 1/r |
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propagating fields direction |
E field in theta direction B field in ø direction |
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poynting vector direction and in terms of Ir |
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maxwell equation in macroscopic media |
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wave equation from maxwell equation when there are no free charges |
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dispersion relation for a macroscopic material. |
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k for a macroscopic material in terms of refraction index |
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k for a dielectric |
k ~ nk0 |
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skin depth |
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conductivity in a plasma |
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polarisation field |
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complex dielectric constant |
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index of refraction |
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equation for alpha that is 2 times the imaginary part of k |
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normal and anomalous dispersion compared to alpha |
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group velocity |
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boundary conditions |
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B field in terms of k and E field |
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conditions of E field |
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refraction coefficient |
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waveguides |
have conducting walls
no free charges or currents inside the waveguide orientated in z direction wave doesn't travel straight inside the waveguide |
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TEM wave |
when both Ez and Bz are zero not allows in waveguide |
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rectangular waveguide with conducting walls |
E parallel =0 B perpendicular =0 |
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wavenumber in a waveguide |
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cut off frequencies in a waveguide |
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why use group velocity instead or phase velocity |
phase velocity is greater than the speed of light |
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coaxial transmission line |
do transmit TEM waves bc core can be held at a different potential to outer wall |
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capacitance and inductance of in coaxial cable |
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impedance in a coaxial cable. |
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impedance mismatch |
if the cable is plugged into a receiver that has a different impedance part of the signal will be reflected back |
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cavity |
black off sides or a metal box Conducting metal plates |
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want frequencies exist inside a cavity |
where a B and d are the side lengths |
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how well can a cavity hold radiation |
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position and momentum 4 vector |
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finding length changes in different reference frames |
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contraction |
sum over 2 repeating indices, one if which is upper and one that is lower |
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lorentz transformation |
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tensor transforms |
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lorentz vector for transforming |
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four vector potential |
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tensor matrix |
used to go to a boosted frame with 2 indices |
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transformation arguments |
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