QUIZ 2 REVISION Flashcards
Polar molecules under external electric field. Will the molecules always align with the electric field?
No. (Graph explanation). There is always random motion that competes against alignment.
Typically the dipole potential energy is much smaller than the thermal energy.
a= p_0 E / k T
How do you define polarization and how is it related to the electric field in linear dielectrics?
Polarization is the mean dipole moment density.
P = X ε_0 E
Write down Maxwell’s equations for linear, isotropic and homogeneous dielectrics.
(LIH)
D = ε_0(1+X)E
P = P = X ε_0 E
ρ_bound = -∇ . P
∇ D = ρ_free
∇ x D = 0 –> D = -ε_0 (1+X)∇V
(Laplace) ∇^2 V = -ρ_free/ε_0(1+X)
In linear dielectrics how are the free and bound charge related?
ρ_bound = ρ_free (1/ε_r - 1)
Why does capacitance go up when you insert dielectrics in a capacitor?
It increases by (1+X) because the electric field decreases (due to polarization (screens out the charges on the plate)) such that the capacitor stores the same charge for a smaller voltage –> increased capacitance.
In which direction is the force on dielectrics that is partially inserted in a capacitor?
Directed towards the inside of the capacitor as the force tries to the fill in the capacitor with dielectric
Describe 3 different behaviours of matter under applied magnetic field
1- Ferromagnetism: strong attraction with all magnetic moments lined up and locked
2- Paramagnetism: weak attraction with permanent magnetic moment -> aligns with the applied Magnetic field
3- Diamagnetism: weak repulsion: no permanent magnetic moment -> B induced to reduce change in B applied, antialigned with Bapp
Why do diamagnetic and paramagnetic matters behave differently?
In diamagnetism the electrons’ spins cancel out and in paramagnetic matters there are permanent magnetic moment due to unpaired electron spins and orbital motions (non zero net circulating current)
Magnetization is determined by the spin and orbital motion of an electron so how is electron magnetic moment related to its angular momemtum?
m is proportional to the angular momemtum
-for electrons m = -e/2m_e J_am
Protons have magnetic moments as well but it is tiny compared to that of electrons, why?
Because protons are more massive
What happens to the magnetic moments when they are misaligned with an applied magnetic field?
Precession occurs
Diamagnetic materials have no intrinsic magnetic moment so what drives the repelling behaviour of diamagnetic material in the presence of external magnetic field?
There is an induced electric field due to change of B with time: B app induces current oriented so as to minimize the change in the field (anti-align)
What should the typical size of intrinsic electron magnetic moment be?
It should be the Bohr’s magneton: μ_B = e hbar/2m_e
Define magnetization
Analogue: Polarization. It is the net magnetic moment per unit volume (a vector)
For paramagnetic material, how does the magnetization depend on the strength of the applied magnetic field and temperature?
M = Nm_0^2Bext/3kT
- larger Bext –> more induced magnetic moment
- colder –> less thermal motion (so less randomization
How are bound currents related to magnetization?
How are bound charges related to polarization?
K_b = M x n for uniform magnetization sigma_b = P dot n
How is the bound current density related to magnetization?
How is the bound charge density related to polarization?
J_b = curl of M
ρ_bound = -∇ . P
Consider a solenoid filled with paramagnetic material. What provides the free current? Which direction is the bound current?
The free current is the current through the solenoid (electrons moving)
The bound current follows the free current. (B is uniform so M is uniform so Jb = 0 so Kb must be in the same direction)
Consider a capacitor filled with dielectrics. What provides the free charges?
Describe the distribution of bound charges.
The free charges are the charges on the plates. (Capacitor plates provide the free charges). The positive charge point towards the negatively charged plate and negative charge point towards the positively charged plate.
Boundary conditions @ dielectric interface?
Boundary conditions @ magnetic interface?
- Discontinuity in perpendicular ( Dout-Din = surface free charge density)
Continuity in parallel (Ein = Eout) - Continuity in perpendicular (Bin = Bout)
Discontinuity in parallel (Hout-Hin = Kfree x n
What is EMF?
It is the electromotive force (net integrated force) so it is actually work ([EMF] = Volts)
Describe the direction of the current within the square loop and explain (B is into the page)
entering: counterclockwise
exiting: clockwise
Self-sustaining dynamo
What happens to the charges on the disk?
In what direction is the induced B?
Charge separation: negative inward and positive outward
In the same direction as Bseed (do a diagram
Solenoid connected to a battery. What is the maximum current I?
What is the characteristic time over which I grows?
V/R
Characteristic time = L/R
