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GRE Physics

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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. 3 Laws of Thermo
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
I = V/R exp(-t/RC)
F = f* (c+v_r)/(c+v_s)
L = mr²d?/dt

2. Astro: Aperture Formula (Rayleigh Criterion)
C_eq = ?C_i
<T> = -<V>/2
.5 LI²
? = 1.22?/D

3. Clausius-Clapeyron Equation
J = ? Fdt
Measurements close to mean
Dp/dt = L / (t ?V)
<T> = -<V>/2

4. Astro: Kepler'S Third Law
X_C = 1/(i?C)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
<?1|?2> = 0 ? Orthogonal
P² ~ R³

5. Adiabatic processes (dS - dQ - P and V)
DS = 0 - dQ = 0 - P V^? = constant
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Always Real
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

6. EM: Bremsstrahlung (translation)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
I = I_0 Cos[?]^2
?~T
Braking Radiation

7. Time Lorentz Transformation
L = L_0 Sqrt[1-v^2/c^2]
? (t-vx/c²)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
C_eq = ?C_i

8. Relativistic length contraction
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/T
L = L_0 Sqrt[1-v^2/c^2]
C_eq = (? 1/C_i)^-1

9. Rocket Thrust
X_C = 1/(i?C)
? (t-vx/c²)
dQ = dW +dU
u dm/dt

10. Thermo: Adiabatic Work vs Isothermal Work
Always Real
A[B -C] + [A -C]B
Q = CVexp(-t/RC)
W_A < W_I

11. Thermo: Monatomic gas ?=?
? = 5/3
dQ = dW +dU
F = s * T4
qvb = mv²/R

12. EM: Electromagnetic inertia
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Always Real
Faraday/Lenz: current inducted opposes the changing field
ih_barL_z

13. Magnetic Field Through Ring
µ0 I / 2R
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
ih_barL_z
M? = 2dsin(?)

14. EM: Method of Images
Z = ?g_i*exp(-E/kT)
I_z = I_x + I_y (think hoop symmetry)
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
Opposing charge induced upon conductor

15. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
NC?T
Dv = -udm/m - v = v0 + u ln(m0/m)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Q = CVexp(-t/RC)

16. Mech: Impulse
(° of Freedom)kT/2
Opposing charge induced upon conductor
E = s/e_0
J = ? Fdt

17. Effective Potential
Always Real
T = I?²/2
V(r) + L²2/2mr²
Asin(?) = m?

18. EM: Lorentz Force
U - ts = -tlog(Z)
L = T - V dL/dq = d/dt dL/dqdot
F = qv×B
1/2 CV²

19. Quant: Expectation Value
I_z = I_x + I_y (think hoop symmetry)
DW/dq
F = µ0 q v I / 2pr
<?|O|?>

20. Electromotive Force
DW/dq
F = µ0 q v I / 2pr
F_f = µ*F_N
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

21. RLC resonance condition
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
I ' = I cos²(?)
C_eq = (? 1/C_i)^-1
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

22. Expectation value of the energy of state |?>
E = Z²*E1
<T> = 1/2 * <dV/dx>
E = <?| H |?>
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

23. Quant: Orthogonality of States
S_mean = s/Sqrt[N]
<?1|?2> = 0 ? Orthogonal
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

24. Lab: Standard Deviation of Poisson
DW/dq
v(mean)
I = I_cm + (1/2)m d^2
Q = CVexp(-t/RC)

25. Lab: Precision of Measurements
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Measurements close to mean
E²-p²c²
Int ( A . dr) = Int ( del x A) dSurface

26. Adiabatic means
Isentropic
(° of Freedom)kT/2
PdV +dU
C = 4pe0 ab/(a-b) = inner and outer radii

27. Thermo: 1st Law
X_L = i?L
?= h/v(2mE)
C_eq = (? 1/C_i)^-1
dQ = dW +dU

28. Mech: Rotational Energy
T = I?²/2
P +1/2 ? v² + ?gh = Constant
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
C = 4pe0 ab/(a-b) = inner and outer radii

29. Quant: Commutator Relation [AB -C]
Braking Radiation
A[B -C] + [A -C]B
S_mean = s/Sqrt[N]
V(r) + L²2/2mr²

30. Kepler'S Three Laws
Z_c = -i/(?C) ; Z_L = i ? L
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
B = µ0 I n
? (t-vx/c²)

31. Hamiltonian and Hamilton'S equations
DS = 0 - dQ = 0 - P V^? = constant
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
?~T
<T> = -<V>/2

32. Atom: Positronium Reduced Mass
I = -(c ?t)^2 + d^2
µ = m_e/2
DS = 0 - dQ = 0 - P V^? = constant
I = I_cm + (1/2)m d^2

33. Double Slit: Interference Minimum - Diffraction Minimum
Ct²-x²-y²-z²
J = ? Fdt
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

34. Work done on a gas
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
?~T
F_f = µ*F_N

35. Relativistic interval (which must remain constant for two events)
ma + kx = 0
L = mr²d?/dt
X_L = i?L
I = -(c ?t)^2 + d^2

36. Springs in series/parallel
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
P/A = s T^4
? exp(-e/t)
dQ = dW +dU

37. Partition Function
I ' = I cos²(?)
F = s * T4
? exp(-e/t)
S_mean = s/Sqrt[N]

38. Work (P - V)
P1V1 - P2V2 / (? - 1)
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.
H = H_0 + ?H
A[B -C] + [A -C]B

39. Boltzmann / Canonical distribution
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
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
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
ds² = (c*dt)² - ?(x_i)²

40. Magnetic Field For Current in Long Wire
µ0 I / 2pR
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
ds² = (c*dt)² - ?(x_i)²
Ct²-x²-y²-z²

41. Kepler'S third law (T and R)
.5 LI²
T^2 = k R^3 - k=constant
I ' = I cos²(?)
J/(ne) n: atom density

42. Stark Effect
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
X_L = X_C or X_total = 0
V(r) + L²2/2mr²
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

43. Perturbations
Asin(?) = m?
C_eq = (? 1/C_i)^-1
H = H_0 + ?H
I = V/R exp(-t/RC)

44. EM: Electric Field inside of Conductor
µ0 I1I2 / (2pd)
4H + 2e- ? He +2? + 6?
B = µ0 I n
0

45. Addition of relativistic velocities

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46. Rayleigh criterion
I = -(c ?t)^2 + d^2
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
? = 1.22? / d
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

47. A reversible process stays..
µ = Current * Area T = µ x B
? exp(-e/t)
L = mr²d?/dt
Infinitely close to equilibrium at all times

48. Triplet/singlet states: symmetry and net spin
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
P +1/2 ? v² + ?gh = Constant
E²-p²c²
P1V1 - P2V2 / (? - 1)

49. Energy in Inductor
.5 LI²
I_z = I_x + I_y (think hoop symmetry)
S_mean = s/Sqrt[N]
? = h/mv

50. Angular momentum - Central Force Motion
Z_c = -i/(?C) ; Z_L = i ? L
J/(ne) n: atom density
L = mr²d?/dt
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i