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GRE Physics

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Answer 50 questions in 15 minutes.
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1. td(entropy) =
?max = 2.898 x 10 -³ / T
PdV +dU
F = R/2
Measurements close to mean

2. Bohr Model: Radii
N²/Z (m_elec/m_red)
L = L_0 Sqrt[1-v^2/c^2]
W_A < W_I
S = k ln[O] ; dS = dQ/T

3. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
Faraday/Lenz: current inducted opposes the changing field
I = I_cm + md²
U - ts = -tlog(Z)

4. Invariant spatial quantity
F = qv×B
Ct²-x²-y²-z²
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Sin(?) = ?/d

5. Single Slit Diffraction Maximum
u dm/dt
<?|O|?>
F = µ0 q v I / 2pr
Asin(?) = m?

6. EM: Reactance of Capacitor
E = <?| H |?>
? = 5/3
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
X_C = 1/(i?C)

7. Polarizers - intensity when crossed at ?
I = I_0 Cos[?]^2
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
N²/Z (m_elec/m_red)
M? = 2dsin(?)

8. Mech: Virial Theorem
<T> = -<V>/2
S = (hbar/2) s ;with S = S_x xhat + S_y yhat + S_z zhat -s = s_x xhat + s_y yhat + s_z zhat
Z = ?g_i*exp(-E/kT)
C = 4pe0 ab/(a-b) = inner and outer radii

9. Angular momentum operators L^2 and L_z
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
E = Z²*E1
V = -L di/dt
Z²/n² (m_red/m_elec)

10. Dulong Petit Law
Braking Radiation
X_L = X_C or X_total = 0
V = -L di/dt
Cv = dE/dT = 3R

11. Relativistic Momentum
1/2 CV²
Always Real
?mv
T = I?²/2

12. Effective Potential
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Z²/n² (m_red/m_elec)
V(r) + L²2/2mr²
ih_barL_z

13. Mech: Centripetal Force
u dm/dt
S_mean = s/Sqrt[N]
F = mv²/r
dU = 0 ? dS = ?dW/T

14. Single Slit Diffraction Intensity
U - ts = -tlog(Z)
Cos[?] Sin[?] -Sin[?] Cos[?]
1/vLC
I = Im (sinc²(a)) ; a = pai sin(?) / ?

15. EM: Method of Images
.5 LI²
Opposing charge induced upon conductor
F = -2*m(? x r)
N d flux / dt

16. Triplet/singlet states: symmetry and net spin
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
? = ?0 root((1-v/c)/(1+v/c))
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

17. Bragg'S Law of Reflection
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
X_L = i?L
M? = 2dsin(?)
F = mv²/r

18. Weighted average (mean and unc. of mean)
Sin(?) = ?/d
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
? = h/p
E = <?| H |?>

19. Thermo: Partition Function
I = I_0 Cos[?]^2
? = ?0 root((1-v/c)/(1+v/c))
Z = ?g_i*exp(-E/kT)
Sin(?) = ?/d

20. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Infinitely close to equilibrium at all times
I = I_cm + (1/2)m d^2
A[B -C] + [A -C]B

21. Commutator identities ( [B -A C] - [A -B] )
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Cos[?] Sin[?] -Sin[?] Cos[?]
When you apply a uniform electric field - it induces a dipole moment and interacts with it - and that effect depends on |mj |. So if j is an integer - splits (asymmetrically) into j+1 levels - and if j is a half integer - splits (asymmetrically) into
µ0 I / 2R

22. Kepler'S Three Laws
Dv = -udm/m - v = v0 + u ln(m0/m)
v(mean)
I = -(c ?t)^2 + d^2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

23. EM: Maxwell'S equations
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Sin(?) = ?/d
J = ? Fdt
V = V0 + V0 a ?T

24. Stefan-Boltzmann law for blackbodies (power per area and T)
ds² = (c*dt)² - ?(x_i)²
P/A = s T^4
Faraday/Lenz: current inducted opposes the changing field
1/2 CV²

25. Magnetic Field Through Ring
µ0 I / 2R
µ=s^2
Int ( A . dr) = Int ( del x A) dSurface
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

26. Compton Scattering
? = 1.22? / d
ih_barL_z
?? = h/mc * (1-cos(?))
I = Im (sinc²(a)) ; a = pai sin(?) / ?

27. EM: Electric Field inside of Conductor
? = 1.22? / d
F_f = µ*F_N
Measurements close to mean
0

28. Clausius-Clapeyron Equation
In Zeeman effect - the contribution of electron spin to total angular momentum means that it isn'T always three lines and they are not always equally spaced.
Asin(?) = m?
? exp(-e/t)
Dp/dt = L / (t ?V)

29. Selection Rules
?s = 0 - ?l = ±1
Infinitely close to equilibrium at all times
?~T
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

30. Focal point of mirrror with curvature
ih_barL_z
4H + 2e- ? He +2? + 6?
? = 5/3
F = R/2

31. EM: SHO (Hooke)
L = mr²d?/dt
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
ma + kx = 0
P² ~ R³

32. RLC resonance condition
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
µ0 I1I2 / (2pd)
E²-p²c²
ih_barL_z

33. Thermo: Average Total Energy
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Cv = dE/dT = 3R
(° of Freedom)kT/2
P/A = s T^4

34. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
I = I_cm + (1/2)m d^2
V(r) + L²2/2mr²
Cos[?] Sin[?] -Sin[?] Cos[?]

35. Partition Function
When you apply a uniform electric field - it induces a dipole moment and interacts with it - and that effect depends on |mj |. So if j is an integer - splits (asymmetrically) into j+1 levels - and if j is a half integer - splits (asymmetrically) into
L = T - V dL/dq = d/dt dL/dqdot
E²-p²c²
? exp(-e/t)

36. Selection rules for atomic transitions
F = mv²/r
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
C_eq = (? 1/C_i)^-1
?? = h/mc * (1-cos(?))

37. Magnetic Dipole Moment and Torque
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
ma + kx = 0
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
µ = Current * Area T = µ x B

38. Anomalous Zeeman Effect

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39. Thermo: Isothermal
dU = 0 ? dS = ?dW/T
J/(ne) n: atom density
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Faraday/Lenz: current inducted opposes the changing field

40. Stoke'S Theorem
µ=s^2
Int ( A . dr) = Int ( del x A) dSurface
I_z = I_x + I_y (think hoop symmetry)
?s = 0 - ?l = ±1

41. Energy in terms of partition function
P² ~ R³
C_eq = (? 1/C_i)^-1
qvb = mv²/R
U = t^2 d/dt (logZ)

42. E field of a capacitor (d->0)
M? = 2dsin(?)
I_z = I_x + I_y (think hoop symmetry)
U = t^2 d/dt (logZ)
E = s/e_0

43. Mech: Rotational Energy
I = I_cm + md²
? = ?0 root((1-v/c)/(1+v/c))
Asin(?) = m?
T = I?²/2

44. Astro: Kepler'S Third Law
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Dp/dt = L / (t ?V)
P² ~ R³
E²-p²c²

45. Rocket Thrust
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
µ0 I / 2R
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
u dm/dt

46. Pauli matrices
C_eq = (? 1/C_i)^-1
S = (hbar/2) s ;with S = S_x xhat + S_y yhat + S_z zhat -s = s_x xhat + s_y yhat + s_z zhat
W' = (w-v)/(1-w v/c^2) ; observer in S sees an object moving at velocity w; another frame S' moves at v wrt S.
X_L = X_C or X_total = 0

47. Wein'S Displacement Law
?max = 2.898 x 10 -³ / T
Cos[?] Sin[?] -Sin[?] Cos[?]
F_f = µ*F_N
? = 5/3

48. 3 Laws of Thermo
? exp(-e/t)
Q = CVexp(-t/RC)
T^2 = k R^3 - k=constant
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

49. Biot-Savart law
I = I_0 Cos[?]^2
?= h/v(2mE)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

50. Complex impedance (expressions for capacitor and inductor)
PdV +dU
Sin(?) = ?/d
Z_c = -i/(?C) ; Z_L = i ? L
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

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