Electromagnetism Flashcards
what is a plasma
collection of positive and negative charges that are net neutral
eg. ionsphere, fluorescent light bulb
dielectric definition
what are polar and non-polar dielectrics
dielectrics produce their own electric field in repsonse to an applied electric field
polar = have permanent dipole moments that rotate in repsonse to an applied E-field
non-polar = displacement of charge that produces dipoles can be in response to an applied E-field
coulombโs law
E = q/(4๐๐0r^2) r_hat
wavelength from wavevector
kreal = 2๐/๐
auxiliary/ electric-displacement field
D = ๐0 E + P
example of application:
D = ๐0 E external = ๐r ๐o E internal
so, ๐r = Eexternal/Einternal
direction of propogation of electric and magnetic fields
E x B
what to do if angle is โabove the equatorial planeโ
halve it
dispersion relation
and equation for phase velocity
k^2 = w^2 ฮผ0 ๐0
v = w/k = 1/sqrt(ฮผ0 ๐0)
condition for propogation
k^2 > 0
therefore, k must be real
what is minimum frequency and dispersion relation of a dielectric waveguide
wmin > (๐c)/(aโ(๐r)) * ((n1)^2+(n2)^2)
((n1๐)/a)^2 + ((n2๐)/a)^2 + k^2 = ฮผ0 ๐ r ๐0 ๐^2
how are the transmission and reflection coefficients associated with an electromagnetic wave crossing a boundary devrived. (fresnelโs equations)
by requiring that maxwellโs equations are met at all points in space and time across the interface between the two media; that the continuity of E and H are met across the interface
how does a radio transmitter radiate electromagnetic waves
the transmitter is an arrangement of conductors that conduct AC current. The current causes charges to accelerate and produce the elctromagnetic waves
is a material a good conductor
from dispersion relation, good conductor if imaginary term > > real term
lorentz force equation
F = BIL
ampereโs law
B = โฆ
B = ฮผ0I/2๐r
Bdl = 2๐rB = ฮผ0* Ienc
(l = circumfrence of wire = 2๐r)
on graph of E-field and B-field, what are the directions
E perp B perp k
(E x B) par k
what is a waveguide
it is a material that confines an electromagnetic wave to propogate in one direction and that generates very little energy loss.
eg. copper tube or guiding microwaves to heat fusion plasma; optical fibre for communications
meissner state in superconductors
B(x) = B 0 exp(-x/lamda)
ho to solve equation of the form: del^2B = (1/a^2) B
exponential solutions where B(x) = B 0 exp(-x/a)
definition of magnectic susceptibility
further, in a cylinder
chi = M/H
in a cylinder: chi = ฮผ0M/Bapplied
where M = IA/V
how does a small penetration depth compared to size affect a super conductor (in terms of magnectic susceptability against temperature)
will have a susceptability closer to zero at T=0, will converge to Tc in the same manor as original penetration depth
maxwellโs equations
del * E = rho/epsilon0
del * B = 0
del x E = - dB/dt
del x B = mu0 J + mu0 epsilon0 dE/dt
dot and cross products
a*b = |a||b|cosฮธ
axb = |a||b|sinฮธ n_hat
unit vector
v_hat = v/|v|
electric potential equation
V = Q/(4๐๐0r)
how to use gaussโ law to find E
E * dS = Q/๐0
gives, |E| = Q/๐0|A|
area current density equations
J = I/area = I/๐R^2
Ienc = area*J = ๐r^2 I/๐R^2 = r^2/(R^2) I
total current I = integral of J
what is the ether
theoretical medium that was thought to permeate all space and transmmit transverse waves (like light). The michelson morley experiemnts showed it doesnโt exist & lead to special relativity
what is the proper frame
frame where there are no forces on charge that are stationary or moving at constant velocity. Time is dilated & space is lorentz corrected for all other frames, when observed from the proper frame.
flux equation
B * dS
gaussโs law
E * dS = sum(q)/๐0
= 1/๐0 (rho * dV) = (del * E dV)
faradayโs law
V = -db/dt * S = d(flux)/dt
biot-savart law
dB = โฆ.
dB = mu0I/(4๐r^2) sinฮธ dl
