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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. Quant: Orthogonality of States
Z²/n² (m_red/m_elec)
? (t-vx/c²)
<?1|?2> = 0 ? Orthogonal
1/ne - where n is charge carrier density

2. Astro: Aperture Formula (Rayleigh Criterion)
S_mean = s/Sqrt[N]
? = 1.22?/D
V(r) + L²2/2mr²
Isentropic

3. Rocket Thrust
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
u dm/dt
µ0 I / 2R
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

4. Rocket Equation
Dv = -udm/m - v = v0 + u ln(m0/m)
F = f* (c+v_r)/(c+v_s)
KE = 1/2 * µ (dr/dt)² L = µ r x v
ds² = (c*dt)² - ?(x_i)²

5. Clausius-Clapeyron Equation
Dp/dt = L / (t ?V)
Opposing charge induced upon conductor
Faraday/Lenz: current inducted opposes the changing field
? = 5/3

6. Magnetic Field Through Ring
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
µ0 I / 2R
F = s * T4
N d flux / dt

7. Magnetic Field of a long solenoid
? = h/p
B = µ0 I n
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
? exp(-e/t)

8. Solid: Resistivity of Semi-Conductor
?~1/T
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
1/ne - where n is charge carrier density
F = R/2

9. A reversible process stays..
Infinitely close to equilibrium at all times
F = µ0 q v I / 2pr
?= h/v(2mE)
C_eq = ?C_i

10. Stoke'S Theorem
Int ( A . dr) = Int ( del x A) dSurface
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
.5 LI²
F = f* (c+v_r)/(c+v_s)

11. Rayleigh criterion
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
I = I_cm + md²
? = 1.22? / d
? exp(-e/t)

12. Lab: Standard Deviation of Poisson
0
v(mean)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
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.

13. Parallel axis theorem
Cos[?] Sin[?] -Sin[?] Cos[?]
Measurements close to true value
DW/dq
I = I_cm + (1/2)m d^2

14. Perpendicular axis theorem
µ = m_e/2
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
I_z = I_x + I_y (think hoop symmetry)
L = T - V dL/dq = d/dt dL/dqdot

15. Astro: Kepler'S Third Law
B = µ0 I n
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
qvb = mv²/R
P² ~ R³

16. EM: Reactance of Inductor
X_L = i?L
C = 4pe0 ab/(a-b) = inner and outer radii
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
F_f = µ*F_N

17. Weighted average (mean and unc. of mean)
U = t^2 d/dt (logZ)
Cos[?] Sin[?] -Sin[?] Cos[?]
X_C = 1/(i?C)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

18. Kepler'S Three Laws
L = T - V dL/dq = d/dt dL/dqdot
P +1/2 ? v² + ?gh = Constant
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Measurements close to true value

19. Focal point of mirrror with curvature
?mv
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.
F = R/2
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

20. Dulong Petit Law
? = 5/3
Cv = dE/dT = 3R
I ' = I cos²(?)
?~T

21. EM: Electromagnetic inertia
I_z = I_x + I_y (think hoop symmetry)
Faraday/Lenz: current inducted opposes the changing field
.5 LI²
F = qv×B

22. Pauli matrices
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
dQ = dW +dU
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
Exp(N(µ-e)/t)

23. Invariant Energy Quantity
E = Z²*E1
E²-p²c²
<?|O|?>
I_z = I_x + I_y (think hoop symmetry)

24. Relativistic interval (which must remain constant for two events)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
F = µ0 q v I / 2pr
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
I = -(c ?t)^2 + d^2

25. Polarizers - intensity when crossed at ?
I = I_0 Cos[?]^2
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
F = R/2
<T> = -<V>/2

26. Single Slit Diffraction Maximum
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Asin(?) = m?

27. Quant: Eigenvalue of Hermitian Operator
PdV +dU
DW = P dV
Always Real
qvb = mv²/R

28. How to derive cylcotron frequency
V = -L di/dt
Dp/dt = L / (t ?V)
qvb = mv²/R
ds² = (c*dt)² - ?(x_i)²

29. EM: Lorentz Force
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
F = qv×B
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Ct²-x²-y²-z²

30. Rayleigh'S Criterion
Sin(?) = ?/d
T = I?²/2
? exp(-e/t)
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.

31. Work in a capacitor
1/2 CV²
KE = 1/2 * µ (dr/dt)² L = µ r x v
?? = h/mc * (1-cos(?))
Braking Radiation

32. Energy levels from the Coulomb potential
Z = ?g_i*exp(-E/kT)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
.5 CV²
P/A = s T^4

33. Triplet/singlet states: symmetry and net spin
?mc²
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
S_mean = s/Sqrt[N]
I = Im (sinc²(a)) ; a = pai sin(?) / ?

34. Atom: Bohr Theory Ionization
X_L = X_C or X_total = 0
DW/dq
Cos[?] Sin[?] -Sin[?] Cos[?]
E = Z²*E1

35. Complex impedance (expressions for capacitor and inductor)
Always Real
ds² = (c*dt)² - ?(x_i)²
Z_c = -i/(?C) ; Z_L = i ? L
B = µ0 I n

36. Bragg'S Law of Reflection
V(r) + L²2/2mr²
dQ = dW +dU
M? = 2dsin(?)
4H + 2e- ? He +2? + 6?

37. Biot-Savart law
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
<?|O|?>
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
KE = 1/2 * µ (dr/dt)² L = µ r x v

38. Force/length between two wires
? = 1.22? / d
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
µ0 I1I2 / (2pd)
Q = CVexp(-t/RC)

39. Relativistic Energy
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
<?1|?2> = 0 ? Orthogonal
?mc²
?s = 0 - ?l = ±1

40. Lagrangian and Lagrange'S equation
µ0 I / 2R
L = T - V dL/dq = d/dt dL/dqdot
? = 1.22? / d
Opposing charge induced upon conductor

41. Helmholtz Free Energy
M? = 2dsin(?)
I = I_0 Cos[?]^2
1/ne - where n is charge carrier density
U - ts = -tlog(Z)

42. Entropy (# of states - and in terms of other thermo quantities)
S = k ln[O] ; dS = dQ/T
Measurements close to true value
µ0 I / 2pR
U = t^2 d/dt (logZ)

43. Bohr Model: Energy
Z²/n² (m_red/m_elec)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
P² ~ R³
<?|O|?>

44. Hamiltonian and Hamilton'S equations
V = -L di/dt
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
? = 1.22? / d

45. RLC resonance condition
S = k ln[O] ; dS = dQ/T
V = V0 + V0 a ?T
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

46. EM: Method of Images
<?|O|?>
Opposing charge induced upon conductor
E = <?| H |?>
DS = 0 - dQ = 0 - P V^? = constant

47. Work (P - V)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
P1V1 - P2V2 / (? - 1)
Hbar*?³/(p²c³exp(hbar?/t)-1)
.5 LI²

48. Selection Rules
NC?T
I = I_0 Cos[?]^2
?s = 0 - ?l = ±1
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

49. QM: de Broglie Wavelength
P/A = s T^4
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
?= h/v(2mE)

50. Electromotive Force
? = 5/3
DW/dq
Exponentially decreasing radial function
P/A = s T^4