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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)
<T> = -<V>/2
S = k ln[O] ; dS = dQ/T
ih_barL_z
F = qv×B

2. EM: SHO (Hooke)
ma + kx = 0
dU = 0 ? dS = ?dW/T
F = qv×B
(3/2) n R ?t

3. Relativistic Momentum
?mv
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
X_C = 1/(i?C)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

4. Resistance - length - area - rho
V = -L di/dt
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
B = µ0 I n

5. Electromotive Force
DW/dq
L = L_0 Sqrt[1-v^2/c^2]
N d flux / dt
DW = P dV

6. Lab: Accuracy of Measurements
? = ?0 root((1-v/c)/(1+v/c))
Measurements close to true value
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Q = CVexp(-t/RC)

7. Partition Function
F = qv×B
? exp(-e/t)
B = µ0 I n
Z = ?g_i*exp(-E/kT)

8. Mech: Centripetal Force
1/ne - where n is charge carrier density
NC?T
F = mv²/r
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

9. Mech: Parallel Axis Theorem (Moment of Inertia)
I = I_cm + md²
Z_c = -i/(?C) ; Z_L = i ? L
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
v(mean)

10. Perpendicular axis theorem
T = I?²/2
E = <?| H |?>
I_z = I_x + I_y (think hoop symmetry)
N²/Z (m_elec/m_red)

11. Atom: Orbital Config
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
u dm/dt
?_max = b/T
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

12. EM: Parallel Capacitance
? = 1.22?/D
C_eq = ?C_i
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

13. EM: Reactance of Capacitor
F = R/2
?mv
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
X_C = 1/(i?C)

14. Work in a capacitor
? (t-vx/c²)
C = 4pe0 ab/(a-b) = inner and outer radii
Infinitely close to equilibrium at all times
1/2 CV²

15. Rocket Equation
Dv = -udm/m - v = v0 + u ln(m0/m)
X_C = 1/(i?C)
F = µ0 q v I / 2pr
? = 1.22? / d

16. Angular momentum - Central Force Motion
Const: 2t = (n +.5)? Destructive 2t = n?
L = mr²d?/dt
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
0

17. Boltzmann / Canonical distribution
.5 LI²
KE = 1/2 * µ (dr/dt)² L = µ r x v
PdV +dU
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

18. Thermo: Partition Function
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
1/vLC
Z = ?g_i*exp(-E/kT)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

19. SR: Total Energy of a Particle
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Ct²-x²-y²-z²
µ=s^2
?max = 2.898 x 10 -³ / T

20. Adiabatic processes (dS - dQ - P and V)
dQ = dW +dU
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)
I = I_cm + md²

21. Astro: p-p Chain
L = L_0 Sqrt[1-v^2/c^2]
ma + kx = 0
? = 5/3
4H + 2e- ? He +2? + 6?

22. Energy in Inductor
.5 LI²
Dp/dt = L / (t ?V)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

23. Ohm'S Law w/ current density
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
J = E s - s = Conductivity - E = Electric field
? exp(-e/t)
F = mv²/r

24. Relativistic length contraction
L = L_0 Sqrt[1-v^2/c^2]
qvb = mv²/R
C = 4pe0 ab/(a-b) = inner and outer radii
Exp(N(µ-e)/t)

25. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
?= h/v(2mE)
.5 LI²
E = Z²*E1

26. Thermo: Blackbody Radiation
F = s * T4
E²-p²c²
µ0 I / 2pR
I = I_0 Cos[?]^2

27. Double Slit: Interference Minimum - Diffraction Minimum
0
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
J/(ne) n: atom density
P² ~ R³

28. EM: Maxwell'S equations
N²/Z (m_elec/m_red)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
? = h/mv
dQ = dW +dU

29. Thermo: Isothermal
Braking Radiation
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
dU = 0 ? dS = ?dW/T
<?1|?2> = 0 ? Orthogonal

30. Source Free RL Circuit
Dv = -udm/m - v = v0 + u ln(m0/m)
Hbar*?³/(p²c³exp(hbar?/t)-1)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
M? = 2dsin(?)

31. Kepler'S Three Laws
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
I = I_cm + (1/2)m d^2
? = 5/3
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

32. Atom: Positronium Reduced Mass
N²/Z (m_elec/m_red)
(3/2) n R ?t
µ = m_e/2
Braking Radiation

33. Rocket Thrust
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.
u dm/dt
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
µ=s^2

34. Lab: Standard Deviation of Poisson
S = k ln[O] ; dS = dQ/T
Cos[?] Sin[?] -Sin[?] Cos[?]
v(mean)
DW = P dV

35. EM: Electric Field inside of Conductor
4H + 2e- ? He +2? + 6?
KE = 1/2 * µ (dr/dt)² L = µ r x v
Cv = dE/dT = 3R
0

36. Bernoulli Equation
P +1/2 ? v² + ?gh = Constant
.5 LI²
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

37. Force on a wire in magnetic field
F_f = µ*F_N
F = I L X B
µ0 I / 2pR
F = mv²/r

38. Poisson distribution (µ and s)
C_eq = ?C_i
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
µ=s^2
Infinitely close to equilibrium at all times

39. Doppler Shift for light
NC?T
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
? = ?0 root((1-v/c)/(1+v/c))
Q = CVexp(-t/RC)

40. Energy levels from the Coulomb potential
4H + 2e- ? He +2? + 6?
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
<?|O|?>

41. Source-free RC Circuit
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
J/(ne) n: atom density
V = -L di/dt
(° of Freedom)kT/2

42. Angular momentum operators L^2 and L_z
µ0 I / 2R
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
dU = 0 ? dS = ?dW/T
I ' = I cos²(?)

43. Stefan-Boltzmann law for blackbodies (power per area and T)
P/A = s T^4
P² ~ R³
ds² = (c*dt)² - ?(x_i)²
u dm/dt

44. Quant: Orthogonality of States
Const: 2t = (n +.5)? Destructive 2t = n?
<?|O|?>
<?1|?2> = 0 ? Orthogonal
W_A < W_I

45. SR: Spacetime Interval
ds² = (c*dt)² - ?(x_i)²
S = k ln[O] ; dS = dQ/T
I = I_cm + md²
U = t^2 d/dt (logZ)

46. Error in the mean if each measurement has the same uncertainty s
µ = m_e/2
1/ne - where n is charge carrier density
Opposing charge induced upon conductor
S_mean = s/Sqrt[N]

47. Current in resistor in RC circuit
H = H_0 + ?H
F = s * T4
I = V/R exp(-t/RC)
X_L = i?L

48. Selection rules for atomic transitions
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
F = I L X B
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

49. Lab: Precision of Measurements
Measurements close to mean
? = h/mv
F = R/2
µ = Current * Area T = µ x B

50. De Broigle Wavelength
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Exp(N(µ-e)/t)
? = h/mv
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?