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
coulombβs law
E = q/(4ππ0r^2) r_hat
wavelength from wavevector
kreal = 2π/π
auxiliary/ electric-displacement field
D = π0 E + P
example of application:
D = π0 E external = πr πo E internal
so, πr = Eexternal/Einternal
direction of propogation of electric and magnetic fields
E x B
what to do if angle is βabove the equatorial planeβ
halve it
dispersion relation
and equation for phase velocity
k^2 = w^2 ΞΌ0 π0
v = w/k = 1/sqrt(ΞΌ0 π0)
condition for propogation
k^2 > 0
therefore, k must be real
what is minimum frequency and dispersion relation of a dielectric waveguide
wmin > (πc)/(aβ(πr)) * ((n1)^2+(n2)^2)
((n1π)/a)^2 + ((n2π)/a)^2 + k^2 = ΞΌ0 π r π0 π^2
how are the transmission and reflection coefficients associated with an electromagnetic wave crossing a boundary devrived. (fresnelβs equations)
by requiring that maxwellβs 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
ampereβs law
B = β¦
B = ΞΌ0I/2πr
Bdl = 2πrB = ΞΌ0* Ienc
(l = circumfrence of wire = 2πr)
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 = ΞΌ0M/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
maxwellβs 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|cosΞΈ
axb = |a||b|sinΞΈ n_hat
unit vector
v_hat = v/|v|
