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GRE Physics

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. Wein'S displacement law for blackbodies (? and T)
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
Infinitely close to equilibrium at all times
?_max = b/T
L = T - V dL/dq = d/dt dL/dqdot

2. Dulong Petit Law
Exp(N(µ-e)/t)
Cv = dE/dT = 3R
Z = ?g_i*exp(-E/kT)
Z_c = -i/(?C) ; Z_L = i ? L

3. Anomalous Zeeman Effect

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4. Rotation matrix (2x2)
Cos[?] Sin[?] -Sin[?] Cos[?]
C_eq = ?C_i
.5 LI²
?= h/v(2mE)

5. EM: Electromagnetic inertia
V = -L di/dt
?mc²
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Faraday/Lenz: current inducted opposes the changing field

6. EM: AC Resonance
?mv
? = 1.22?/D
µ0 I / 2pR
X_L = X_C or X_total = 0

7. Atom: Orbital Config
V(r) + L²2/2mr²
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
v(mean)
I = I_cm + (1/2)m d^2

8. Mech: Virial Theorem
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
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
Cv = dE/dT = 3R
<T> = -<V>/2

9. Astro: p-p Chain
4H + 2e- ? He +2? + 6?
? = 1.22?/D
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.
L = T - V dL/dq = d/dt dL/dqdot

10. Solid: Resistivity of Semi-Conductor
X_C = 1/(i?C)
F = mv²/r
F = s * T4
?~1/T

11. Energy in Inductor
.5 LI²
.5 CV²
N d flux / dt
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

12. De Broglie wavelength
µ0 I1I2 / (2pd)
? = h/p
.5 LI²
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

13. Invariant spatial quantity
J = ? Fdt
Ct²-x²-y²-z²
µ = Current * Area T = µ x B
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

14. Astro: Aperture Formula (Rayleigh Criterion)
? = 1.22?/D
Z = ?g_i*exp(-E/kT)
DS = 0 - dQ = 0 - P V^? = constant
E²-p²c²

15. Planck Radiation Law
I = Im (sinc²(a)) ; a = pai sin(?) / ?
F = mv²/r
Hbar*?³/(p²c³exp(hbar?/t)-1)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

16. Angular momentum - Central Force Motion
L = mr²d?/dt
X_L = X_C or X_total = 0
4H + 2e- ? He +2? + 6?
F = f* (c+v_r)/(c+v_s)

17. Selection Rules
F_f = µ*F_N
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
?s = 0 - ?l = ±1
ds² = (c*dt)² - ?(x_i)²

18. td(entropy) =
U = t^2 d/dt (logZ)
Infinitely close to equilibrium at all times
PdV +dU
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

19. Doppler Shift in Frequency
1/vLC
T = I?²/2
U = t^2 d/dt (logZ)
F = f* (c+v_r)/(c+v_s)

20. Charge in Capacitor
?mc²
? = 1.22?/D
Q = CVexp(-t/RC)
dU = 0 ? dS = ?dW/T

21. Heat added
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
? = 1.22? / d
NC?T
P/A = s T^4

22. Rocket Thrust
u dm/dt
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
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
P1V1 - P2V2 / (? - 1)

23. Bernoulli Equation
P +1/2 ? v² + ?gh = Constant
E = <?| H |?>
Exp(N(µ-e)/t)
Z²/n² (m_red/m_elec)

24. Rayleigh'S Criterion
Sin(?) = ?/d
DW/dq
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
dU = 0 ? dS = ?dW/T

25. Lab: Precision of Measurements
Measurements close to mean
Sin(?) = ?/d
?mv
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

26. Helmholtz Free Energy
I_z = I_x + I_y (think hoop symmetry)
U - ts = -tlog(Z)
F = µ0 q v I / 2pr
X_L = X_C or X_total = 0

27. Boltzmann / Canonical distribution
? = 1.22? / d
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
T = I?²/2

28. SR: Total Energy of a Particle
F = qv×B
U = t^2 d/dt (logZ)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
.5 LI²

29. Thermo: 1st Law
Infinitely close to equilibrium at all times
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
dQ = dW +dU

30. Mean electron drift speed
M? = 2dsin(?)
E = <?| H |?>
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
J/(ne) n: atom density

31. How to derive cylcotron frequency
µ0 I / 2R
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Always Real
qvb = mv²/R

32. Relativistic Energy
T = I?²/2
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
?~1/T
?mc²

33. Bohr Model: Radii
F = I L X B
N²/Z (m_elec/m_red)
F = -2*m(? x r)
P1V1 - P2V2 / (? - 1)

34. Delta Function Potential - type of WF
Dv = -udm/m - v = v0 + u ln(m0/m)
T^2 = k R^3 - k=constant
?= h/v(2mE)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

35. EM: Electric Field inside of Conductor
S_mean = s/Sqrt[N]
KE = 1/2 * µ (dr/dt)² L = µ r x v
0
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

36. Stoke'S Theorem
ih_barL_z
Exp(N(µ-e)/t)
Int ( A . dr) = Int ( del x A) dSurface
I = -(c ?t)^2 + d^2

37. Commutator identities ( [B -A C] - [A -B] )
V = V0 + V0 a ?T
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
v(mean)
u dm/dt

38. Polarizers - intensity when crossed at ?
F = -2*m(? x r)
P/A = s T^4
I = I_0 Cos[?]^2
? = h/mv

39. Energy in terms of partition function
S_mean = s/Sqrt[N]
<?1|?2> = 0 ? Orthogonal
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
U = t^2 d/dt (logZ)

40. Doppler shift for light
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
dU = 0 ? dS = ?dW/T
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
? = 5/3

41. Doppler Shift for light
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
? = ?0 root((1-v/c)/(1+v/c))
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
µ0 I1I2 / (2pd)

42. Lensmaker Equation - Thin Lens
Const: 2t = (n +.5)? Destructive 2t = n?
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
N d flux / dt
(° of Freedom)kT/2

43. Atom: Bohr Theory Ionization
<?1|?2> = 0 ? Orthogonal
E = Z²*E1
?mc²
Faraday/Lenz: current inducted opposes the changing field

44. Triplet/singlet states: symmetry and net spin
µ0 I / 2pR
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
I = I_cm + md²

45. Thermo: Monatomic gas ?=?
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
? = 5/3
Isentropic

46. Magnetic Field of a long solenoid
B = µ0 I n
Q = CVexp(-t/RC)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
? = ?0 root((1-v/c)/(1+v/c))

47. Relativistic interval (which must remain constant for two events)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
I = -(c ?t)^2 + d^2
I = I_cm + (1/2)m d^2

48. Force exerted on charge by long wire
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
F = µ0 q v I / 2pr
?? = h/mc * (1-cos(?))
? = 1.22? / d

49. Weighted average (mean and unc. of mean)
W_A < W_I
dQ = dW +dU
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

50. Work (P - V)
?mv
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
P1V1 - P2V2 / (? - 1)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i