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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. Entropy (# of states - and in terms of other thermo quantities)
S = k ln[O] ; dS = dQ/T
DW/dq
A[B -C] + [A -C]B
Always Real

2. Energy in terms of partition function
E = <?| H |?>
U = t^2 d/dt (logZ)
F = -2*m(? x r)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

3. SR: Spacetime Interval
U - ts = -tlog(Z)
I = V/R exp(-t/RC)
ds² = (c*dt)² - ?(x_i)²
Ct²-x²-y²-z²

4. Atom: Positronium Reduced Mass
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
µ = m_e/2
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
0

5. RLC resonance condition
I = V/R exp(-t/RC)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
I ' = I cos²(?)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

6. Bernoulli Equation
? = 1.22?/D
I = -(c ?t)^2 + d^2
P +1/2 ? v² + ?gh = Constant
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

7. Stoke'S Theorem
Int ( A . dr) = Int ( del x A) dSurface
F_f = µ*F_N
Z²/n² (m_red/m_elec)
Z_c = -i/(?C) ; Z_L = i ? L

8. Doppler shift for light
<T> = 1/2 * <dV/dx>
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
<T> = -<V>/2

9. Work done on a gas
ds² = (c*dt)² - ?(x_i)²
DW = P dV
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
DW/dq

10. Wein'S displacement law for blackbodies (? and T)
Q = CVexp(-t/RC)
?_max = b/T
v(mean)
F = -2*m(? x r)

11. Parallel axis theorem
I = I_cm + (1/2)m d^2
F = qv×B
B = µ0 I n
?~T

12. Mean electron drift speed
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
F = I L X B
J/(ne) n: atom density
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

13. Helmholtz Free Energy
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
F_f = µ*F_N
1/vLC
U - ts = -tlog(Z)

14. Anomalous Zeeman Effect

15. Charge in Capacitor
Q = CVexp(-t/RC)
Cos[?] Sin[?] -Sin[?] Cos[?]
Ct²-x²-y²-z²
I ' = I cos²(?)

16. Pauli matrices
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.
<T> = 1/2 * <dV/dx>
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
ma + kx = 0

17. Kepler'S third law (T and R)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
? = 1.22?/D
<T> = 1/2 * <dV/dx>
T^2 = k R^3 - k=constant

18. Rocket Thrust
E²-p²c²
Asin(?) = m?
C_eq = (? 1/C_i)^-1
u dm/dt

19. Volumetric Expansion
F = µ0 q v I / 2pr
V = V0 + V0 a ?T
I = I_cm + md²
Exp(N(µ-e)/t)

20. Kepler'S Three Laws
F = s * T4
.5 CV²
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

21. Single Slit Diffraction Intensity
? (t-vx/c²)
I = Im (sinc²(a)) ; a = pai sin(?) / ?
?? = h/mc * (1-cos(?))
P² ~ R³

22. Double Slit: Interference Minimum - Diffraction Minimum
? = 1.22? / d
I = I_cm + (1/2)m d^2
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
<T> = 1/2 * <dV/dx>

23. EM: AC Resonance
?mv
Hbar*?³/(p²c³exp(hbar?/t)-1)
X_L = X_C or X_total = 0
Z_c = -i/(?C) ; Z_L = i ? L

24. Atom: Bohr Formula
X_L = i?L
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Ct²-x²-y²-z²
Dv = -udm/m - v = v0 + u ln(m0/m)

25. EM: Bremsstrahlung (translation)
E²-p²c²
Braking Radiation
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

26. Mech: Parallel Axis Theorem (Moment of Inertia)
I = I_cm + md²
.5 CV²
Ct²-x²-y²-z²
Always Real

27. Internal Energy of an Ideal Gas
T^2 = k R^3 - k=constant
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
A[B -C] + [A -C]B
(3/2) n R ?t

28. Commutator identities ( [B -A C] - [A -B] )
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Hbar*?³/(p²c³exp(hbar?/t)-1)
I ' = I cos²(?)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

29. Radiation (Larmor - and another neat fact)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Infinitely close to equilibrium at all times
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

30. Perpendicular axis theorem
I_z = I_x + I_y (think hoop symmetry)
E²-p²c²
NC?T
?max = 2.898 x 10 -³ / T

31. EM: Lorentz Force
N d flux / dt
F = qv×B
L = mr²d?/dt
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

32. Atom: Bohr Theory Ionization
E = Z²*E1
<T> = 1/2 * <dV/dx>
0
C_eq = ?C_i

33. Perturbations
H = H_0 + ?H
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
A[B -C] + [A -C]B

34. How to derive cylcotron frequency
µ=s^2
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
0
qvb = mv²/R

35. Center of Mass: Kinetic Energy & Angular Momentum
<?1|?2> = 0 ? Orthogonal
? = 1.22?/D
KE = 1/2 * µ (dr/dt)² L = µ r x v
H = H_0 + ?H

36. Coriolis Force
H = H_0 + ?H
V = V0 + V0 a ?T
F = -2*m(? x r)
? = h/p

37. E field of a capacitor (d->0)
Int ( A . dr) = Int ( del x A) dSurface
v(mean)
E = s/e_0
? (t-vx/c²)

38. Clausius-Clapeyron Equation
J = ? Fdt
Dp/dt = L / (t ?V)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

39. First law of thermodynamics (explain direction of energy for each term)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
F = mv²/r

40. De Broglie wavelength
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
(3/2) n R ?t
? = h/p
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

41. Lensmaker Equation - Thin Lens
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
I_z = I_x + I_y (think hoop symmetry)
dU = 0 ? dS = ?dW/T
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

42. Boltzmann / Canonical distribution
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Q = CVexp(-t/RC)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
U = t^2 d/dt (logZ)

43. Force/length between two wires
P² ~ R³
NC?T
µ0 I1I2 / (2pd)
Measurements close to mean

44. Inductance of Solenoid
? = 1.22?/D
µ=s^2
?mc²
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

45. Work (P - V)
P1V1 - P2V2 / (? - 1)
Asin(?) = m?
Sin(?) = ?/d
0

46. Biot-Savart law
µ0 I1I2 / (2pd)
? exp(-e/t)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
F = s * T4

47. EM: Method of Images
J/(ne) n: atom density
Opposing charge induced upon conductor
I = I_cm + md²
Z²/n² (m_red/m_elec)

48. Hamiltonian and Hamilton'S equations
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

49. Energy in a Capacitor
Measurements close to true value
.5 CV²
E = Z²*E1
0

50. Selection rules for atomic transitions
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
µ = Current * Area T = µ x B
dQ = dW +dU
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length