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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. Doppler shift for light
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
?s = 0 - ?l = ±1
N²/Z (m_elec/m_red)
I = -(c ?t)^2 + d^2

2. Poisson distribution (µ and s)
Always Real
I ' = I cos²(?)
Dp/dt = L / (t ?V)
µ=s^2

3. Thermo: 1st Law
Measurements close to true value
F = µ0 q v I / 2pr
dQ = dW +dU
Measurements close to mean

4. Angular momentum operators L^2 and L_z
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Dp/dt = L / (t ?V)
I = V/R exp(-t/RC)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

5. Force on a wire in magnetic field
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
?~T
C_eq = ?C_i
F = I L X B

6. Addition of relativistic velocities

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7. Adiabatic means
L = T - V dL/dq = d/dt dL/dqdot
Dv = -udm/m - v = v0 + u ln(m0/m)
Isentropic
P/A = s T^4

8. Relativistic Energy
?mc²
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
V = V0 + V0 a ?T
Q = CVexp(-t/RC)

9. Rocket Equation
DS = 0 - dQ = 0 - P V^? = constant
X_L = i?L
E = Z²*E1
Dv = -udm/m - v = v0 + u ln(m0/m)

10. Adiabatic processes (dS - dQ - P and V)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Cv = dE/dT = 3R
DS = 0 - dQ = 0 - P V^? = constant
A[B -C] + [A -C]B

11. Compton Scattering
?? = h/mc * (1-cos(?))
µ=s^2
?_max = b/T
P/A = s T^4

12. How to derive cylcotron frequency
Hbar*?³/(p²c³exp(hbar?/t)-1)
T^2 = k R^3 - k=constant
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
qvb = mv²/R

13. Kepler'S third law (T and R)
.5 CV²
µ0 I / 2pR
T^2 = k R^3 - k=constant
µ = m_e/2

14. Magnetic Field For Current in Long Wire
E = s/e_0
I ' = I cos²(?)
F = f* (c+v_r)/(c+v_s)
µ0 I / 2pR

15. Thermo: Blackbody Radiation
Z²/n² (m_red/m_elec)
F = s * T4
Asin(?) = m?
I = I_0 Cos[?]^2

16. Lab: Standard Deviation of Poisson
B = µ0 I n
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
v(mean)
ds² = (c*dt)² - ?(x_i)²

17. Lensmaker Equation - Thin Lens
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
?? = h/mc * (1-cos(?))
Z_c = -i/(?C) ; Z_L = i ? L

18. Invariant Energy Quantity
E²-p²c²
S = k ln[O] ; dS = dQ/T
F_f = µ*F_N
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

19. Source Free RL Circuit
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
M? = 2dsin(?)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

20. EM: Electric Field inside of Conductor
µ=s^2
dU = 0 ? dS = ?dW/T
0
V = V0 + V0 a ?T

21. Thermo: Monatomic gas ?=?
X_L = X_C or X_total = 0
<?|O|?>
? = 5/3
? = ?0 root((1-v/c)/(1+v/c))

22. EM: Lorentz Force
Cos[?] Sin[?] -Sin[?] Cos[?]
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
PdV +dU
F = qv×B

23. Coriolis Force
Z²/n² (m_red/m_elec)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
F = -2*m(? x r)
u dm/dt

24. Perpendicular axis theorem
(3/2) n R ?t
L = T - V dL/dq = d/dt dL/dqdot
I_z = I_x + I_y (think hoop symmetry)
F = s * T4

25. EM: Series Capacitance
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
dU = 0 ? dS = ?dW/T
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
C_eq = (? 1/C_i)^-1

26. Bohr Model: Radii
µ = Current * Area T = µ x B
N²/Z (m_elec/m_red)
Int ( A . dr) = Int ( del x A) dSurface
?~T

27. Energy levels from the Coulomb potential
V = -L di/dt
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Infinitely close to equilibrium at all times
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

28. Helmholtz Free Energy
U - ts = -tlog(Z)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
v(mean)
PdV +dU

29. Invariant spatial quantity
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
F = µ0 q v I / 2pr
N²/Z (m_elec/m_red)
Ct²-x²-y²-z²

30. Resistance - length - area - rho
H = H_0 + ?H
?= h/v(2mE)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

31. Malus Law

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32. Work in a capacitor
F = f* (c+v_r)/(c+v_s)
1/2 CV²
L = T - V dL/dq = d/dt dL/dqdot
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

33. Polarizers - intensity when crossed at ?
<?1|?2> = 0 ? Orthogonal
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.
I = I_0 Cos[?]^2
Hbar*?³/(p²c³exp(hbar?/t)-1)

34. Quant: Eigenvalue of Hermitian Operator
.5 LI²
KE = 1/2 * µ (dr/dt)² L = µ r x v
S = k ln[O] ; dS = dQ/T
Always Real

35. Rayleigh criterion
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 = qv×B
? = 1.22? / d
Isentropic

36. EM: SHO (Hooke)
ma + kx = 0
C_eq = ?C_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.
Dv = -udm/m - v = v0 + u ln(m0/m)

37. Atom: Hydrogen Wave Function Type
µ=s^2
F = f* (c+v_r)/(c+v_s)
Exponentially decreasing radial function
?? = h/mc * (1-cos(?))

38. Relativistic Momentum
?mv
? = h/mv
C_eq = (? 1/C_i)^-1
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

39. Law of Mass Action
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.
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Exp(N(µ-e)/t)
?mv

40. Quant: Commutator Relation [AB -C]
A[B -C] + [A -C]B
F = R/2
Q = CVexp(-t/RC)
0

41. Mech: Parallel Axis Theorem (Moment of Inertia)
Opposing charge induced upon conductor
J = E s - s = Conductivity - E = Electric field
I = I_cm + md²
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

42. Rayleigh'S Criterion
S = k ln[O] ; dS = dQ/T
Sin(?) = ?/d
M? = 2dsin(?)
T^2 = k R^3 - k=constant

43. Stark Effect
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
<?1|?2> = 0 ? Orthogonal
ma + kx = 0
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

44. Planck Radiation Law
Measurements close to true value
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Hbar*?³/(p²c³exp(hbar?/t)-1)

45. Gibbs Factor
dU = 0 ? dS = ?dW/T
Exp(N(µ-e)/t)
P² ~ R³
T^2 = k R^3 - k=constant

46. Stoke'S Theorem
B = µ0 I n
I = I_cm + (1/2)m d^2
Int ( A . dr) = Int ( del x A) dSurface
?mc²

47. Lagrangian and Lagrange'S equation
F = µ0 q v I / 2pr
V = -L di/dt
F = s * T4
L = T - V dL/dq = d/dt dL/dqdot

48. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
qvb = mv²/R
M? = 2dsin(?)
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.

49. EM: Bremsstrahlung (translation)
Braking Radiation
I = I_0 Cos[?]^2
L = mr²d?/dt
dU = 0 ? dS = ?dW/T

50. Astro: Aperture Formula (Rayleigh Criterion)
dU = 0 ? dS = ?dW/T
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
(3/2) n R ?t
? = 1.22?/D