Magnetism
What is Ampere's Law and what do you use it for?
int (B dot dl) = mu_0 I_enc
Find magnetic field from the enclose current
What is Gauss's Law?
int E dot da= Qenc/epsilon_0
What is the probability of a state (phi) being in a wavefunction (psi)?
P=|<phi|psi>|^2/<psi|psi>
What is the inertia equation for the xx and the xy terms?
I_xx = int (y^2 +z^2) dm, I_xy= - int(xy)) dm
How to find the uncertainty of position operator?
del x = sqrt{<x^2>-<x>^2}
What is the equation for the poynting vector?
S=(1/mu_0) E cross B
What is the equation for the electric flux?
int E dot dA
How do you find the new state (phi) if you proejct 1 state (v_1) onto a wavefunction (psi)?
|phi>=|v1><v1|psi>
What is a way to write the centrifugal force?
F=mv^2/r=m omega^2 r
What is the force in magnetic field using current?
F = int ( I (dl cross B))
What is A_dip?
A_dip = (mu_0/4 pi) (m cross r hat)/r^2
mangetic vector potential dipole term
What is the polarization density? Then how can you find the electric displacement from that?
P=Xepsilon_0 E (volumnistic density of dipole moments in dielectric material)
Then D=epsilon_0 E +P
What is the Hamiltonian operator for the x axis?
- (hbar^2/2m)(d^2/dx^2)
What is the equation for the Coriolis force?
F_c = -2m(omega cross v)
What is sin and cos in small angle approximation?
sintheta=theta, costheta=1
B = del cross A
What is a way to find the current from charge and angular frequency?
I=Q/T=Q omega/2pi
What is one solution to the schrodinger equation if you have a square well?
Psi = Acoskx+Bsinkx, Psi = A exp(ikx)+Bexp(-ikx)
How to find the normal modes of a system?
Find kinetic energy of the system
Find potential energy of the system
Set up the matrices for K and U
Find the matrix for V-omega^2*T, and find the determinant of that matrix.
Solve the determinant for omega to find the normal frequencies (using the quadratic formula)
Substitute omega squared back into the matrix, solve the systems of equations to find the normal modes (eigenvectors)
L = r cross g, where g = epsiolon_0 (E cross B)
What is the Biot-Savart Law?
B= (mu_0/4pi) int I(dl cross r hat)/r^2
What is the electric potential dipole term?
V+dip = (1/4pi epsilon_0) (p dot rhat)/r^2
What does is mean if two operators commute?
[A,B]=AB-BA=0
If two operators commute, their observables are said to be compatible and both quantities can be measured at the same time with infinite precision.
What are inertia equations for a rod?
For pivot at COM, I =1/12ML^2. Pivot on one end, I=1/3ML^2
What is the equation for energy density and how does it related to the poynting vector?
u = 1/2 (epsilon_0 E^2 + 1/mu_0 B^2)