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GRE Physics

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Ohm'S Law w/ current density
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
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
J = E s - s = Conductivity - E = Electric field
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

2. 3 Laws of Thermo
Cos[?] Sin[?] -Sin[?] Cos[?]
?mv
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
<T> = -<V>/2

3. Charge in Capacitor
I ' = I cos²(?)
C = 4pe0 ab/(a-b) = inner and outer radii
E = Z²*E1
Q = CVexp(-t/RC)

4. Weighted average (mean and unc. of mean)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
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.
DW = P dV
.5 CV²

5. Force exerted on charge by long wire
F = µ0 q v I / 2pr
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
1/ne - where n is charge carrier density
X_L = i?L

6. Mech: Centripetal Force
P² ~ R³
ma + kx = 0
I = V/R exp(-t/RC)
F = mv²/r

7. Thermo: Partition Function
Z = ?g_i*exp(-E/kT)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
? = h/mv
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

8. Lab: Accuracy of Measurements
Braking Radiation
Hbar*?³/(p²c³exp(hbar?/t)-1)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Measurements close to true value

9. Gibbs Factor
E²-p²c²
Measurements close to mean
Z_c = -i/(?C) ; Z_L = i ? L
Exp(N(µ-e)/t)

10. Self Inductance
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
ih_barL_z
V = -L di/dt
Opposing charge induced upon conductor

11. Adiabatic processes (dS - dQ - P and V)
PdV +dU
Z_c = -i/(?C) ; Z_L = i ? L
DS = 0 - dQ = 0 - P V^? = constant
1/vLC

12. Mech: Parallel Axis Theorem (Moment of Inertia)
I = I_cm + md²
Faraday/Lenz: current inducted opposes the changing field
T^2 = k R^3 - k=constant
Q = CVexp(-t/RC)

13. Doppler shift for light
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
P +1/2 ? v² + ?gh = Constant
L = mr²d?/dt
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

14. Spherical Capacitor Equation
C = 4pe0 ab/(a-b) = inner and outer radii
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
?mv
0

15. Polarizers - intensity when crossed at ?
F = R/2
Exp(N(µ-e)/t)
I = I_0 Cos[?]^2
C_eq = (? 1/C_i)^-1

16. Energy in terms of partition function
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
U = t^2 d/dt (logZ)
V = V0 + V0 a ?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

17. Lab: Precision of Measurements
dU = 0 ? dS = ?dW/T
Measurements close to mean
(3/2) n R ?t
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

18. Triplet/singlet states: symmetry and net spin
Measurements close to true value
Exp(N(µ-e)/t)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
(° of Freedom)kT/2

19. Source-free RC Circuit
I = I_0 Cos[?]^2
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
<?|O|?>
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

20. Wein'S Displacement Law
?max = 2.898 x 10 -³ / T
Always Real
<?|O|?>
dQ = dW +dU

21. E field of a capacitor (d->0)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
I = I_cm + (1/2)m d^2
E = s/e_0
S = k ln[O] ; dS = dQ/T

22. Lagrangian and Lagrange'S equation
L = T - V dL/dq = d/dt dL/dqdot
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
L = mr²d?/dt
V = V0 + V0 a ?T

23. Perpendicular axis theorem
T = I?²/2
µ = Current * Area T = µ x B
I_z = I_x + I_y (think hoop symmetry)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

24. td(entropy) =
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Q = CVexp(-t/RC)
1/2 CV²
PdV +dU

25. Thermo: Adiabatic Work vs Isothermal Work
?s = 0 - ?l = ±1
W_A < W_I
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
?max = 2.898 x 10 -³ / T

26. Energy in Inductor
.5 LI²
<T> = 1/2 * <dV/dx>
F_f = µ*F_N
L = T - V dL/dq = d/dt dL/dqdot

27. Dulong Petit Law
P/A = s T^4
Cv = dE/dT = 3R
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 / 2pR

28. Current in resistor in RC circuit
N d flux / dt
Measurements close to true value
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
I = V/R exp(-t/RC)

29. Solid: Resistivity of Semi-Conductor
Int ( A . dr) = Int ( del x A) dSurface
?~1/T
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
F = µ0 q v I / 2pr

30. Work in a capacitor
1/2 CV²
X_C = 1/(i?C)
?s = 0 - ?l = ±1
1/ne - where n is charge carrier density

31. Atom: Positronium Reduced Mass
µ = m_e/2
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Braking Radiation

32. Work (P - V)
P1V1 - P2V2 / (? - 1)
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
?mc²

33. Complex impedance (expressions for capacitor and inductor)
4H + 2e- ? He +2? + 6?
Z_c = -i/(?C) ; Z_L = i ? L
X_C = 1/(i?C)
I = -(c ?t)^2 + d^2

34. Doppler Shift in Frequency
.5 LI²
?~1/T
? exp(-e/t)
F = f* (c+v_r)/(c+v_s)

35. Bragg'S Law of Reflection
µ0 I / 2pR
? = ?0 root((1-v/c)/(1+v/c))
M? = 2dsin(?)
S_mean = s/Sqrt[N]

36. Selection Rules
C = 4pe0 ab/(a-b) = inner and outer radii
? = 1.22?/D
F = µ0 q v I / 2pr
?s = 0 - ?l = ±1

37. First law of thermodynamics (explain direction of energy for each term)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
1/2 CV²
dU = 0 ? dS = ?dW/T

38. Stefan-Boltzmann law for blackbodies (power per area and T)
L = L_0 Sqrt[1-v^2/c^2]
F = R/2
P/A = s T^4
NC?T

39. Quant: Commutator Relation [AB -C]
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Braking Radiation
Opposing charge induced upon conductor
A[B -C] + [A -C]B

40. Time Lorentz Transformation
F = R/2
? (t-vx/c²)
Exp(N(µ-e)/t)
Dp/dt = L / (t ?V)

41. EM: Reactance of Inductor
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.
?~1/T
?mc²
X_L = i?L

42. Malus Law

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43. EM: Lorentz Force
F = qv×B
4H + 2e- ? He +2? + 6?
1/vLC
DW = P dV

44. Focal point of mirrror with curvature
F = R/2
Cos[?] Sin[?] -Sin[?] Cos[?]
Const: 2t = (n +.5)? Destructive 2t = n?
DW = P dV

45. Clausius-Clapeyron Equation
<?1|?2> = 0 ? Orthogonal
Dp/dt = L / (t ?V)
DW/dq
?~1/T

46. Delta Function Potential - type of WF
Cv = dE/dT = 3R
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
1/2 CV²

47. QM: de Broglie Wavelength
?= h/v(2mE)
I = V/R exp(-t/RC)
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
E = <?| H |?>

48. Resistance - length - area - rho
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Int ( A . dr) = Int ( del x A) dSurface
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Z_c = -i/(?C) ; Z_L = i ? L

49. How to derive cylcotron frequency
µ0 I1I2 / (2pd)
qvb = mv²/R
S_mean = s/Sqrt[N]
1/2 CV²

50. Rayleigh criterion
? = 1.22? / d
<T> = 1/2 * <dV/dx>
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
F = -2*m(? x r)