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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. Work done on a gas
µ0 I / 2R
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
DW = P dV

2. Quant: Orthogonality of States
Asin(?) = m?
I = I_cm + md²
<?1|?2> = 0 ? Orthogonal
u dm/dt

3. Mech: Force of Friction
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
F_f = µ*F_N
B = µ0 I n
J/(ne) n: atom density

4. td(entropy) =
4H + 2e- ? He +2? + 6?
C_eq = ?C_i
PdV +dU
Q = CVexp(-t/RC)

5. Resonance frequency of LC circuit
1/vLC
E²-p²c²
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

6. Helmholtz Free Energy
0
U - ts = -tlog(Z)
Hbar*?³/(p²c³exp(hbar?/t)-1)
I = I_cm + (1/2)m d^2

7. Coriolis Force
DS = 0 - dQ = 0 - P V^? = constant
J = E s - s = Conductivity - E = Electric field
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
F = -2*m(? x r)

8. Doppler Shift for light
dQ = dW +dU
? = h/p
? = ?0 root((1-v/c)/(1+v/c))
v(mean)

9. Electromotive Force
DW/dq
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
L = L_0 Sqrt[1-v^2/c^2]
(3/2) n R ?t

10. Polarizers - intensity when crossed at ?
V(r) + L²2/2mr²
I = I_0 Cos[?]^2
J = ? Fdt
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.

11. Single Slit Diffraction Intensity
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
1/vLC
? = 1.22? / d

12. Law of Mass Action
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
F_f = µ*F_N
X_L = X_C or X_total = 0
Measurements close to true value

13. Lab: Standard Deviation of Poisson
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
C_eq = (? 1/C_i)^-1
Const: 2t = (n +.5)? Destructive 2t = n?
v(mean)

14. Rocket Thrust
u dm/dt
?? = h/mc * (1-cos(?))
? = 5/3
F = qv×B

15. Planck Radiation Law
C_eq = ?C_i
? exp(-e/t)
Hbar*?³/(p²c³exp(hbar?/t)-1)
T = I?²/2

16. Addition of relativistic velocities

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17. Biot-Savart law
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
? = ?0 root((1-v/c)/(1+v/c))
F = µ0 q v I / 2pr
?~1/T

18. Atom: Positronium Reduced Mass
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
µ = m_e/2
Measurements close to mean
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

19. Selection rules for atomic transitions
H = H_0 + ?H
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
P² ~ R³
J/(ne) n: atom density

20. Complex impedance (expressions for capacitor and inductor)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Z_c = -i/(?C) ; Z_L = i ? L
DW = P dV
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

21. Mech: Virial Theorem
I = V/R exp(-t/RC)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
<T> = -<V>/2
F = f* (c+v_r)/(c+v_s)

22. Energy in terms of partition function
F = I L X B
? = h/p
U = t^2 d/dt (logZ)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

23. Parallel axis theorem
C_eq = (? 1/C_i)^-1
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
I = I_cm + (1/2)m d^2
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

24. Astro: Kepler'S Third Law
µ0 I / 2R
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
u dm/dt
P² ~ R³

25. SR: Total Energy of a Particle
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
v(mean)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
? = 1.22?/D

26. Quant: Eigenvalue of Hermitian Operator
NC?T
Always Real
Infinitely close to equilibrium at all times
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

27. De Broigle Wavelength
µ0 I / 2R
? = h/mv
F = µ0 q v I / 2pr
Opposing charge induced upon conductor

28. Rocket Equation
Dv = -udm/m - v = v0 + u ln(m0/m)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
µ = m_e/2

29. Bohr Model: Energy
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Z²/n² (m_red/m_elec)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
<T> = -<V>/2

30. Thermo: Average Total Energy
(° of Freedom)kT/2
F = mv²/r
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
µ=s^2

31. Lab: Accuracy of Measurements
I_z = I_x + I_y (think hoop symmetry)
U - ts = -tlog(Z)
Measurements close to true value
(° of Freedom)kT/2

32. De Broglie wavelength
S = k ln[O] ; dS = dQ/T
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
? = h/p
V = V0 + V0 a ?T

33. Kepler'S Three Laws
(° of Freedom)kT/2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Const: 2t = (n +.5)? Destructive 2t = n?
I = -(c ?t)^2 + d^2

34. How to derive cylcotron frequency
qvb = mv²/R
B = µ0 I n
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Infinitely close to equilibrium at all times

35. Springs in series/parallel
Dp/dt = L / (t ?V)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Measurements close to true value
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

36. Quant: [L_x -L_y] = ?
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
(3/2) n R ?t
W_A < W_I
ih_barL_z

37. Virial Theorem
V(r) + L²2/2mr²
?? = h/mc * (1-cos(?))
<T> = 1/2 * <dV/dx>
Cv = dE/dT = 3R

38. Magnetic field due to a segment of wire
dQ = dW +dU
B = µ0 I n
µ0 I / 2R
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

39. Charge in Capacitor
µ0 I1I2 / (2pd)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
U - ts = -tlog(Z)
Q = CVexp(-t/RC)

40. Quant: Commutator Relation [AB -C]
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
A[B -C] + [A -C]B
(3/2) n R ?t
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

41. Clausius-Clapeyron Equation
F = µ0 q v I / 2pr
H = H_0 + ?H
? = 1.22?/D
Dp/dt = L / (t ?V)

42. Bernoulli Equation
?mv
?~T
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
P +1/2 ? v² + ?gh = Constant

43. Mech: Rotational Energy
1/ne - where n is charge carrier density
B = µ0 I n
P +1/2 ? v² + ?gh = Constant
T = I?²/2

44. EM: Bremsstrahlung (translation)
X_C = 1/(i?C)
Z = ?g_i*exp(-E/kT)
Braking Radiation
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

45. Lab: Precision of Measurements
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
C_eq = ?C_i
Measurements close to mean
L = mr²d?/dt

46. Bohr Model: Radii
?= h/v(2mE)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
N²/Z (m_elec/m_red)
Isentropic

47. Source-free RC Circuit
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
I ' = I cos²(?)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
DW = P dV

48. EM: Parallel Capacitance
ds² = (c*dt)² - ?(x_i)²
E = <?| H |?>
C_eq = ?C_i
C_eq = (? 1/C_i)^-1

49. Resistance - length - area - rho
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
F = R/2
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

50. Perturbations
Braking Radiation
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
U = t^2 d/dt (logZ)
H = H_0 + ?H