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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. Mech: Virial Theorem
<T> = -<V>/2
Sin(?) = ?/d
Z_c = -i/(?C) ; Z_L = i ? L
F = s * T4

2. Invariant spatial quantity
Ct²-x²-y²-z²
Infinitely close to equilibrium at all times
Z = ?g_i*exp(-E/kT)
? exp(-e/t)

3. Energy in terms of partition function
Dv = -udm/m - v = v0 + u ln(m0/m)
C_eq = ?C_i
v(mean)
U = t^2 d/dt (logZ)

4. Atom: Orbital Config
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
F = qv×B
1/vLC

5. Source Free RL Circuit
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
P1V1 - P2V2 / (? - 1)
E = <?| H |?>
I = -(c ?t)^2 + d^2

6. Thermo: Monatomic gas ?=?
N d flux / dt
? = 5/3
DW/dq
Dp/dt = L / (t ?V)

7. De Broigle Wavelength
J/(ne) n: atom density
J = ? Fdt
µ0 I / 2pR
? = h/mv

8. Resistance - length - area - rho
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
µ=s^2
?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

9. Rayleigh criterion
1/ne - where n is charge carrier density
M? = 2dsin(?)
NC?T
? = 1.22? / d

10. Quant: Eigenvalue of Hermitian Operator
Always Real
L = T - V dL/dq = d/dt dL/dqdot
I = I_0 Cos[?]^2
V(r) + L²2/2mr²

11. Source-free RC Circuit
V = V0 + V0 a ?T
Sin(?) = ?/d
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
µ0 I / 2pR

12. Stefan-Boltzmann law for blackbodies (power per area and T)
P/A = s T^4
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Dp/dt = L / (t ?V)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

13. Force/length between two wires
F = s * T4
PdV +dU
Ct²-x²-y²-z²
µ0 I1I2 / (2pd)

14. Boltzmann / Canonical distribution
L = T - V dL/dq = d/dt dL/dqdot
X_C = 1/(i?C)
S_mean = s/Sqrt[N]
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

15. Energy in a Capacitor
J/(ne) n: atom density
.5 CV²
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
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.

16. Volumetric Expansion
Asin(?) = m?
v(mean)
H = H_0 + ?H
V = V0 + V0 a ?T

17. Rocket Thrust
?mv
u dm/dt
<T> = -<V>/2
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

18. Anomalous Zeeman Effect

19. Entropy (# of states - and in terms of other thermo quantities)
?max = 2.898 x 10 -³ / T
P +1/2 ? v² + ?gh = Constant
S = k ln[O] ; dS = dQ/T
F = mv²/r

20. Energy levels from the Coulomb potential
µ = m_e/2
ds² = (c*dt)² - ?(x_i)²
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
Exp(N(µ-e)/t)

21. Compton Scattering
?max = 2.898 x 10 -³ / T
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
E²-p²c²
?? = h/mc * (1-cos(?))

22. Bragg'S Law of Reflection
M? = 2dsin(?)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Int ( A . dr) = Int ( del x A) dSurface

23. Planck Radiation Law
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Hbar*?³/(p²c³exp(hbar?/t)-1)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

24. Radiation (Larmor - and another neat fact)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
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.
V = -L di/dt
J/(ne) n: atom density

25. Bernoulli Equation
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
W_A < W_I
T = I?²/2
P +1/2 ? v² + ?gh = Constant

26. Wein'S Displacement Law
DW/dq
J/(ne) n: atom density
?max = 2.898 x 10 -³ / T
W_A < W_I

27. Kepler'S third law (T and R)
Braking Radiation
µ = Current * Area T = µ x B
F_f = µ*F_N
T^2 = k R^3 - k=constant

28. Kepler'S Three Laws
Cv = dE/dT = 3R
L = mr²d?/dt
F = µ0 q v I / 2pr
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

29. Quant: Expectation Value
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
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.
<?|O|?>
?~T

30. EM: Electric Field inside of Conductor
E = s/e_0
F = R/2
0
Infinitely close to equilibrium at all times

31. Polarizers - intensity when crossed at ?
? = h/mv
F = qv×B
I = I_0 Cos[?]^2
Dp/dt = L / (t ?V)

32. Thermo: Blackbody Radiation
0
? = ?0 root((1-v/c)/(1+v/c))
F = s * T4
I_z = I_x + I_y (think hoop symmetry)

33. Bohr Model: Energy
Z²/n² (m_red/m_elec)
Z_c = -i/(?C) ; Z_L = i ? L
<?|O|?>
P1V1 - P2V2 / (? - 1)

34. Mech: Centripetal Force
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
F = mv²/r
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

35. Atom: Positronium Reduced Mass
<T> = 1/2 * <dV/dx>
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
µ = m_e/2
F = -2*m(? x r)

36. Gibbs Factor
Exp(N(µ-e)/t)
F = µ0 q v I / 2pr
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
L = mr²d?/dt

37. Relativistic interval (which must remain constant for two events)
I = -(c ?t)^2 + d^2
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
DW = P dV
ds² = (c*dt)² - ?(x_i)²

38. RLC resonance condition
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
C = 4pe0 ab/(a-b) = inner and outer radii
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
PdV +dU

39. Clausius-Clapeyron Equation
Dp/dt = L / (t ?V)
L = T - V dL/dq = d/dt dL/dqdot
?= h/v(2mE)
? = 1.22?/D

40. Helmholtz Free Energy
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
F = s * T4
U - ts = -tlog(Z)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

41. Induced EMF of solenoid
N d flux / dt
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
I = V/R exp(-t/RC)
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

42. EM: Reactance of Inductor
X_L = i?L
dU = 0 ? dS = ?dW/T
Dv = -udm/m - v = v0 + u ln(m0/m)
DW/dq

43. Perpendicular axis theorem
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
F = -2*m(? x r)
I_z = I_x + I_y (think hoop symmetry)
4H + 2e- ? He +2? + 6?

44. A reversible process stays..
Infinitely close to equilibrium at all times
Opposing charge induced upon conductor
X_L = i?L
N²/Z (m_elec/m_red)

45. Magnetic Field of a long solenoid
I_z = I_x + I_y (think hoop symmetry)
S = k ln[O] ; dS = dQ/T
?_max = b/T
B = µ0 I n

46. Quant: Orthogonality of States
A[B -C] + [A -C]B
? = 1.22?/D
<?1|?2> = 0 ? Orthogonal
Z_c = -i/(?C) ; Z_L = i ? L

47. First law of thermodynamics (explain direction of energy for each term)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
µ = Current * Area T = µ x B
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Measurements close to mean

48. Angular momentum - Central Force Motion
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Measurements close to true value
L = mr²d?/dt
Asin(?) = m?

49. Spherical Capacitor Equation
Measurements close to true value
?mc²
C = 4pe0 ab/(a-b) = inner and outer radii
Asin(?) = m?

50. Hamiltonian and Hamilton'S equations
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 = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)