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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. Lagrangian and Lagrange'S equation
Hbar*?³/(p²c³exp(hbar?/t)-1)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
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

2. Quant: Expectation Value
1/2 CV²
<?|O|?>
C_eq = ?C_i
J = E s - s = Conductivity - E = Electric field

3. Triplet/singlet states: symmetry and net spin
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
ma + kx = 0
? exp(-e/t)
(° of Freedom)kT/2

4. QM: de Broglie Wavelength
?= h/v(2mE)
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.
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

5. E field of a capacitor (d->0)
E = s/e_0
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
PdV +dU
? = ?0 root((1-v/c)/(1+v/c))

6. Lab: Standard Deviation of Poisson
v(mean)
I = I_cm + (1/2)m d^2
Cv = dE/dT = 3R
dU = 0 ? dS = ?dW/T

7. Thermo: Blackbody Radiation
C_eq = (? 1/C_i)^-1
Cv = dE/dT = 3R
F = s * T4
?? = h/mc * (1-cos(?))

8. Wein'S displacement law for blackbodies (? and T)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
?_max = b/T

9. Lab: Precision of Measurements
Dv = -udm/m - v = v0 + u ln(m0/m)
A[B -C] + [A -C]B
V = V0 + V0 a ?T
Measurements close to mean

10. Hall Coefficient
Sin(?) = ?/d
1/ne - where n is charge carrier density
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.
(3/2) n R ?t

11. Anomalous Zeeman Effect

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12. EM: Parallel Capacitance
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.
S = k ln[O] ; dS = dQ/T
?mc²
C_eq = ?C_i

13. Source-free RC Circuit
4H + 2e- ? He +2? + 6?
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
µ = m_e/2
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

14. Source Free RL Circuit
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
(° of Freedom)kT/2
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
W_A < W_I

15. Radiation (Larmor - and another neat fact)
<?|O|?>
?~1/T
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

16. RLC resonance condition
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
? = h/p
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

17. SR: Total Energy of a Particle
? = 5/3
P/A = s T^4
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

18. Volumetric Expansion
Cv = dE/dT = 3R
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
µ0 I / 2pR
V = V0 + V0 a ?T

19. EM: AC Resonance
?max = 2.898 x 10 -³ / T
U - ts = -tlog(Z)
X_L = X_C or X_total = 0
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

20. Quant: Commutator Relation [AB -C]
Exp(N(µ-e)/t)
A[B -C] + [A -C]B
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
S_mean = s/Sqrt[N]

21. Inductance of Solenoid
E²-p²c²
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
E = Z²*E1

22. 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)
ma + kx = 0
? = ?0 root((1-v/c)/(1+v/c))
Hbar*?³/(p²c³exp(hbar?/t)-1)

23. Doppler shift for light
Exponentially decreasing radial function
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
P +1/2 ? v² + ?gh = Constant
?= h/v(2mE)

24. Adiabatic processes (dS - dQ - P and V)
Braking Radiation
DS = 0 - dQ = 0 - P V^? = constant
E²-p²c²
Exp(N(µ-e)/t)

25. Poisson distribution (µ and s)
µ=s^2
U - ts = -tlog(Z)
Infinitely close to equilibrium at all times
dQ = dW +dU

26. Mech: Parallel Axis Theorem (Moment of Inertia)
X_C = 1/(i?C)
4H + 2e- ? He +2? + 6?
I = I_cm + md²
0

27. Lensmaker Equation - Thin Lens
ma + kx = 0
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Faraday/Lenz: current inducted opposes the changing field
F = mv²/r

28. Relativistic length contraction
<?|O|?>
L = L_0 Sqrt[1-v^2/c^2]
F = qv×B
Faraday/Lenz: current inducted opposes the changing field

29. Atom: Bohr Theory Ionization
E = Z²*E1
µ0 I / 2R
dU = 0 ? dS = ?dW/T
E = s/e_0

30. Work (P - V)
DS = 0 - dQ = 0 - P V^? = constant
4H + 2e- ? He +2? + 6?
P1V1 - P2V2 / (? - 1)
<?|O|?>

31. Pauli matrices
0
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
µ = Current * Area T = µ x B
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

32. Bragg'S Law of Reflection
4H + 2e- ? He +2? + 6?
Exp(N(µ-e)/t)
M? = 2dsin(?)
Isentropic

33. Self Inductance
Int ( A . dr) = Int ( del x A) dSurface
?= h/v(2mE)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
V = -L di/dt

34. Partition Function
1/ne - where n is charge carrier density
µ = Current * Area T = µ x B
? exp(-e/t)
dQ = dW +dU

35. Lab: Accuracy of Measurements
Measurements close to true value
I = I_cm + md²
Always Real
Int ( A . dr) = Int ( del x A) dSurface

36. Magnetic Field Through Ring
?~1/T
µ0 I / 2R
? = 1.22? / d
I_z = I_x + I_y (think hoop symmetry)

37. Energy in Inductor
Ct²-x²-y²-z²
.5 LI²
ds² = (c*dt)² - ?(x_i)²
I = I_0 Cos[?]^2

38. Kepler'S Three Laws
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))
DS = 0 - dQ = 0 - P V^? = constant
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

39. Heat added
?~1/T
NC?T
E²-p²c²
Hbar*?³/(p²c³exp(hbar?/t)-1)

40. Rayleigh'S Criterion
Exp(N(µ-e)/t)
Sin(?) = ?/d
1/2 CV²
? = ?0 root((1-v/c)/(1+v/c))

41. How to derive cylcotron frequency
qvb = mv²/R
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
4H + 2e- ? He +2? + 6?
F_f = µ*F_N

42. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
E = s/e_0
I = Im (sinc²(a)) ; a = pai sin(?) / ?
J/(ne) n: atom density

43. Atom: Hydrogen Wave Function Type
N d flux / dt
Exponentially decreasing radial function
? = h/mv
? (t-vx/c²)

44. Dulong Petit Law
X_C = 1/(i?C)
?_max = b/T
Cv = dE/dT = 3R
<T> = -<V>/2

45. Work done on a gas
I = I_0 Cos[?]^2
DW = P dV
C_eq = (? 1/C_i)^-1
1/vLC

46. Selection Rules
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
?s = 0 - ?l = ±1
X_L = X_C or X_total = 0
Exponentially decreasing radial function

47. Biot-Savart law
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
Q = CVexp(-t/RC)
X_C = 1/(i?C)

48. Single Slit Diffraction Intensity
I = Im (sinc²(a)) ; a = pai sin(?) / ?
1/2 CV²
Z²/n² (m_red/m_elec)
NC?T

49. Error in the mean if each measurement has the same uncertainty s
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
S_mean = s/Sqrt[N]
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
<T> = 1/2 * <dV/dx>

50. Force on a wire in magnetic field
F = I L X B
Opposing charge induced upon conductor
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
V = V0 + V0 a ?T