Electromagnetism

Question 1

what is a plasma

Answer 1

collection of positive and negative charges that are net neutral
eg. ionsphere, fluorescent light bulb

Question 2

dielectric definition
what are polar and non-polar dielectrics

Answer 2

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

Question 3

coulomb’s law

Answer 3

E = q/(4𝜋𝜖0r^2) r_hat

Question 4

wavelength from wavevector

Answer 4

kreal = 2𝜋/𝜆

Question 5

auxiliary/ electric-displacement field

Answer 5

D = 𝜀0 E + P
example of application:
D = 𝜀0 E external = 𝜀r 𝜀o E internal
so, 𝜀r = Eexternal/Einternal

Question 6

direction of propogation of electric and magnetic fields

Answer 6

E x B

Question 7

what to do if angle is ‘above the equatorial plane’

Answer 7

halve it

Question 8

dispersion relation
and equation for phase velocity

Answer 8

k^2 = w^2 μ0 𝜖0
v = w/k = 1/sqrt(μ0 𝜖0)

Question 9

condition for propogation

Answer 9

k^2 > 0
therefore, k must be real

Question 10

what is minimum frequency and dispersion relation of a dielectric waveguide

Answer 10

wmin > (𝜋c)/(a√(𝜀r)) * ((n1)^2+(n2)^2)

((n1𝜋)/a)^2 + ((n2𝜋)/a)^2 + k^2 = μ0 𝜀 r 𝜖0 𝜔^2

Question 11

how are the transmission and reflection coefficients associated with an electromagnetic wave crossing a boundary devrived. (fresnel’s equations)

Answer 11

by requiring that maxwell’s 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

Question 12

how does a radio transmitter radiate electromagnetic waves

Answer 12

the transmitter is an arrangement of conductors that conduct AC current. The current causes charges to accelerate and produce the elctromagnetic waves

Question 13

is a material a good conductor

Answer 13

from dispersion relation, good conductor if imaginary term > > real term

Question 14

lorentz force equation

Answer 14

F = BIL

Question 15

ampere’s law
B = …

Answer 15

B = μ0I/2𝜋r

Bdl = 2𝜋rB = μ0* Ienc
(l = circumfrence of wire = 2𝜋r)

Question 16

on graph of E-field and B-field, what are the directions

Answer 16

E perp B perp k
(E x B) par k

Question 17

what is a waveguide

Answer 17

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

Question 18

meissner state in superconductors

Answer 18

B(x) = B 0 exp(-x/lamda)

Question 19

ho to solve equation of the form: del^2B = (1/a^2) B

Answer 19

exponential solutions where B(x) = B 0 exp(-x/a)

Question 20

definition of magnectic susceptibility
further, in a cylinder

Answer 20

chi = M/H
in a cylinder: chi = μ0M/Bapplied

where M = IA/V

Question 21

how does a small penetration depth compared to size affect a super conductor (in terms of magnectic susceptability against temperature)

Answer 21

will have a susceptability closer to zero at T=0, will converge to Tc in the same manor as original penetration depth

Question 22

maxwell’s equations

Answer 22

del * E = rho/epsilon0
del * B = 0
del x E = - dB/dt
del x B = mu0 J + mu0 epsilon0 dE/dt

Question 23

dot and cross products

Answer 23

a*b = |a||b|cosθ
axb = |a||b|sinθ n_hat

Question 24

unit vector

Answer 24

v_hat = v/|v|

Question 25

electric potential equation

Answer 25

V = Q/(4𝜋𝜖0r)

Question 26

how to use gauss’ law to find E

Answer 26

E * dS = Q/𝜖0
gives, |E| = Q/𝜖0|A|

Question 27

area current density equations

Answer 27

J = I/area = I/𝜋R^2
Ienc = area*J = 𝜋r^2 I/𝜋R^2 = r^2/(R^2) I

total current I = integral of J

Question 28

what is the ether

Answer 28

theoretical medium that was thought to permeate all space and transmmit transverse waves (like light). The michelson morley experiemnts showed it doesn’t exist & lead to special relativity

Question 29

what is the proper frame

Answer 29

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.

Question 30

flux equation

Answer 30

B * dS

Question 31

gauss’s law

Answer 31

E * dS = sum(q)/𝜖0
= 1/𝜖0 (rho * dV) = (del * E dV)

Question 32

faraday’s law

Answer 32

V = -db/dt * S = d(flux)/dt

Question 33

biot-savart law
dB = ….

Answer 33

dB = mu0I/(4𝜋r^2) sinθ dl