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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. Relativistic Energy
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
I = I_cm + (1/2)m d^2
P² ~ R³
?mc²

2. Angular momentum operators L^2 and L_z
Cv = dE/dT = 3R
Measurements close to true value
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
F = µ0 q v I / 2pr

3. Relativistic length contraction
C_eq = (? 1/C_i)^-1
L = L_0 Sqrt[1-v^2/c^2]
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.
ds² = (c*dt)² - ?(x_i)²

4. Thermo: Average Total Energy
?~T
(° of Freedom)kT/2
Sin(?) = ?/d
? = 5/3

5. A reversible process stays..
NC?T
u dm/dt
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Infinitely close to equilibrium at all times

6. Bohr Model: Radii
P² ~ R³
V(r) + L²2/2mr²
N²/Z (m_elec/m_red)
µ0 I1I2 / (2pd)

7. Single Slit Diffraction Intensity
1/2 CV²
E = s/e_0
I = Im (sinc²(a)) ; a = pai sin(?) / ?
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

8. Lensmaker Equation - Thin Lens
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
F = µ0 q v I / 2pr
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

9. Current in resistor in RC circuit
I = V/R exp(-t/RC)
? (t-vx/c²)
Braking Radiation
U - ts = -tlog(Z)

10. Effective Potential
V(r) + L²2/2mr²
F = qv×B
J = E s - s = Conductivity - E = Electric field
?= h/v(2mE)

11. Rayleigh'S Criterion
Sin(?) = ?/d
?? = h/mc * (1-cos(?))
µ0 I / 2pR
Asin(?) = m?

12. Anomalous Zeeman Effect

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13. Focal point of mirrror with curvature
F = -2*m(? x r)
F = R/2
I = V/R exp(-t/RC)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

14. Magnetic field due to a segment of wire
I = V/R exp(-t/RC)
µ = Current * Area T = µ x B
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

15. Force exerted on charge by long wire
N d flux / dt
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
E = Z²*E1
F = µ0 q v I / 2pr

16. Doppler Shift for light
? = ?0 root((1-v/c)/(1+v/c))
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
PdV +dU
Dp/dt = L / (t ?V)

17. Stoke'S Theorem
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Int ( A . dr) = Int ( del x A) dSurface
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
I ' = I cos²(?)

18. Stefan-Boltzmann law for blackbodies (power per area and T)
µ0 I / 2pR
Always Real
P/A = s T^4
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

19. Coriolis Force
F = -2*m(? x r)
ih_barL_z
Cv = dE/dT = 3R
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

20. Thermo: Monatomic gas ?=?
? = 5/3
Infinitely close to equilibrium at all times
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Dp/dt = L / (t ?V)

21. Magnetic Field For Current in Long Wire
<T> = -<V>/2
µ0 I / 2pR
µ=s^2
T = I?²/2

22. Planck Radiation Law
?_max = b/T
? = 1.22?/D
Hbar*?³/(p²c³exp(hbar?/t)-1)
C_eq = (? 1/C_i)^-1

23. Mech: Rotational Energy
Cos[?] Sin[?] -Sin[?] Cos[?]
Int ( A . dr) = Int ( del x A) dSurface
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
T = I?²/2

24. Hall Coefficient
? exp(-e/t)
1/ne - where n is charge carrier density
?_max = b/T
1/2 CV²

25. SR: Spacetime Interval
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.
F = mv²/r
W_A < W_I
ds² = (c*dt)² - ?(x_i)²

26. Rotation matrix (2x2)
<?1|?2> = 0 ? Orthogonal
X_L = i?L
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Cos[?] Sin[?] -Sin[?] Cos[?]

27. Atom: Bohr Formula
? = 1.22? / d
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
H = H_0 + ?H
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

28. Astro: Aperture Formula (Rayleigh Criterion)
F = -2*m(? x r)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
?_max = b/T
? = 1.22?/D

29. Astro: Kepler'S Third Law
?~T
T = I?²/2
P² ~ R³
I_z = I_x + I_y (think hoop symmetry)

30. De Broigle Wavelength
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
C = 4pe0 ab/(a-b) = inner and outer radii
? = h/mv
v(mean)

31. Rocket Equation
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
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
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Dv = -udm/m - v = v0 + u ln(m0/m)

32. Magnetic Dipole Moment and Torque
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
µ = Current * Area T = µ x B
Exponentially decreasing radial function
.5 CV²

33. Quant: Orthogonality of States
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
<?1|?2> = 0 ? Orthogonal
V = V0 + V0 a ?T
?max = 2.898 x 10 -³ / T

34. Resonance frequency of LC circuit
F = f* (c+v_r)/(c+v_s)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
F = mv²/r
1/vLC

35. Weighted average (mean and unc. of mean)
?~T
qvb = mv²/R
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

36. Atom: Orbital Config
Cv = dE/dT = 3R
ih_barL_z
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
u dm/dt

37. Mean electron drift speed
X_L = X_C or X_total = 0
N²/Z (m_elec/m_red)
J/(ne) n: atom density
Infinitely close to equilibrium at all times

38. Inductance of Solenoid
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
T^2 = k R^3 - k=constant
4H + 2e- ? He +2? + 6?
ds² = (c*dt)² - ?(x_i)²

39. Expectation value of the energy of state |?>
L = T - V dL/dq = d/dt dL/dqdot
E = <?| H |?>
F = s * T4
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

40. Atom: Positronium Reduced Mass
?mc²
Dv = -udm/m - v = v0 + u ln(m0/m)
µ = m_e/2
E = <?| H |?>

41. Relativistic interval (which must remain constant for two events)
I = -(c ?t)^2 + d^2
Z²/n² (m_red/m_elec)
V(r) + L²2/2mr²
? = 5/3

42. Magnetic Field Through Ring
dQ = dW +dU
I_z = I_x + I_y (think hoop symmetry)
µ0 I / 2R
0

43. EM: SHO (Hooke)
4H + 2e- ? He +2? + 6?
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
ma + kx = 0

44. Thermo: Blackbody Radiation
Q = CVexp(-t/RC)
F = s * T4
X_C = 1/(i?C)
1/2 CV²

45. Mech: Virial Theorem
P² ~ R³
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
<T> = -<V>/2
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

46. Induced EMF of solenoid
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
N d flux / dt
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Q = CVexp(-t/RC)

47. Energy in terms of partition function
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
U = t^2 d/dt (logZ)
Infinitely close to equilibrium at all times

48. Boltzmann / Canonical distribution
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
F = I L X B
A[B -C] + [A -C]B
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

49. Thermo: Partition Function
C_eq = ?C_i
X_C = 1/(i?C)
Z = ?g_i*exp(-E/kT)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

50. Helmholtz Free Energy
E = <?| H |?>
<?|O|?>
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
U - ts = -tlog(Z)