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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. Solid: Resistivity of Metal
F = mv²/r
?~T
KE = 1/2 * µ (dr/dt)² L = µ r x v
T^2 = k R^3 - k=constant

2. Triplet/singlet states: symmetry and net spin
DW = P dV
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
<T> = 1/2 * <dV/dx>
Dv = -udm/m - v = v0 + u ln(m0/m)

3. Entropy (# of states - and in terms of other thermo quantities)
Measurements close to true value
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
<?|O|?>
S = k ln[O] ; dS = dQ/T

4. Selection Rules
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
? = 5/3
P +1/2 ? v² + ?gh = Constant
?s = 0 - ?l = ±1

5. EM: Reactance of Capacitor
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
X_C = 1/(i?C)
DW = P dV
4H + 2e- ? He +2? + 6?

6. Quant: [L_x -L_y] = ?
ih_barL_z
Always Real
I = I_0 Cos[?]^2
4H + 2e- ? He +2? + 6?

7. Relativistic interval (which must remain constant for two events)
I ' = I cos²(?)
I = -(c ?t)^2 + d^2
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
1/2 CV²

8. EM: AC Resonance
B = µ0 I n
X_L = X_C or X_total = 0
V(r) + L²2/2mr²
I = -(c ?t)^2 + d^2

9. Radiation (Larmor - and another neat fact)
P/A = s T^4
U = t^2 d/dt (logZ)
NC?T
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

10. Quant: Expectation Value
ds² = (c*dt)² - ?(x_i)²
PdV +dU
.5 LI²
<?|O|?>

11. Electromotive Force
Exp(N(µ-e)/t)
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.
DW/dq
S_mean = s/Sqrt[N]

12. Astro: Aperture Formula (Rayleigh Criterion)
? = 1.22?/D
?~T
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
E = Z²*E1

13. A reversible process stays..
L = mr²d?/dt
J = ? Fdt
I = I_cm + md²
Infinitely close to equilibrium at all times

14. SR: Spacetime Interval
Exponentially decreasing radial function
?mc²
ds² = (c*dt)² - ?(x_i)²
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

15. Stoke'S Theorem
T = I?²/2
4H + 2e- ? He +2? + 6?
Int ( A . dr) = Int ( del x A) dSurface
C_eq = (? 1/C_i)^-1

16. First law of thermodynamics (explain direction of energy for each term)
?~1/T
?mv
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

17. Source Free RL Circuit
Exponentially decreasing radial function
Exp(N(µ-e)/t)
ds² = (c*dt)² - ?(x_i)²
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

18. Compton Scattering
?? = h/mc * (1-cos(?))
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
<?1|?2> = 0 ? Orthogonal
?mc²

19. Thin Film Theory: Constructive / Destructive Interference
S_mean = s/Sqrt[N]
Const: 2t = (n +.5)? Destructive 2t = n?
I = Im (sinc²(a)) ; a = pai sin(?) / ?
H = H_0 + ?H

20. Induced EMF of solenoid
N d flux / dt
I_z = I_x + I_y (think hoop symmetry)
J = ? Fdt
L = L_0 Sqrt[1-v^2/c^2]

21. Invariant spatial quantity
Cos[?] Sin[?] -Sin[?] Cos[?]
qvb = mv²/R
Ct²-x²-y²-z²
F = s * T4

22. Energy levels from the Coulomb potential
dQ = dW +dU
T^2 = k R^3 - k=constant
C = 4pe0 ab/(a-b) = inner and outer radii
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

23. Work done on a gas
.5 CV²
DW = P dV
J = ? Fdt
U - ts = -tlog(Z)

24. Angular momentum - Central Force Motion
N²/Z (m_elec/m_red)
L = mr²d?/dt
C = 4pe0 ab/(a-b) = inner and outer radii
<T> = -<V>/2

25. Adiabatic means
Const: 2t = (n +.5)? Destructive 2t = n?
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Isentropic
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

26. Springs in series/parallel
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Exponentially decreasing radial function
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
F = -2*m(? x r)

27. Rayleigh'S Criterion
.5 CV²
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Sin(?) = ?/d
F = mv²/r

28. EM: Electric Field inside of Conductor
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.
0
F = µ0 q v I / 2pr
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

29. Resistance - length - area - rho
Faraday/Lenz: current inducted opposes the changing field
Braking Radiation
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
P1V1 - P2V2 / (? - 1)

30. Single Slit Diffraction Intensity
I = Im (sinc²(a)) ; a = pai sin(?) / ?
N²/Z (m_elec/m_red)
Q = CVexp(-t/RC)
µ0 I / 2pR

31. Heat added
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Dp/dt = L / (t ?V)
? = 5/3
NC?T

32. Force exerted on charge by long wire
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
F = µ0 q v I / 2pr
? exp(-e/t)
Cos[?] Sin[?] -Sin[?] Cos[?]

33. Volumetric Expansion
F = qv×B
V = V0 + V0 a ?T
?~T
Z_c = -i/(?C) ; Z_L = i ? L

34. Biot-Savart law
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
B = µ0 I n
Opposing charge induced upon conductor
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

35. Bar magnets -- direction of B field lines - earth'S B field
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
C = 4pe0 ab/(a-b) = inner and outer radii
V = V0 + V0 a ?T
?~T

36. Error in the mean if each measurement has the same uncertainty s
I_z = I_x + I_y (think hoop symmetry)
X_C = 1/(i?C)
S_mean = s/Sqrt[N]
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

37. Double Slit: Interference Minimum - Diffraction Minimum
1/2 CV²
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
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

38. td(entropy) =
Measurements close to true value
C_eq = ?C_i
PdV +dU
F = qv×B

39. EM: Lorentz Force
T = I?²/2
?max = 2.898 x 10 -³ / T
I = V/R exp(-t/RC)
F = qv×B

40. Bohr Model: Radii
? = h/mv
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
ma + kx = 0
N²/Z (m_elec/m_red)

41. Mean electron drift speed
ma + kx = 0
?_max = b/T
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
J/(ne) n: atom density

42. Quant: Commutator Relation [AB -C]
?_max = b/T
<?1|?2> = 0 ? Orthogonal
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
A[B -C] + [A -C]B

43. Energy in Inductor
? = 1.22?/D
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
.5 LI²
µ0 I / 2pR

44. EM: Reactance of Inductor
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
X_L = i?L
H = H_0 + ?H
DS = 0 - dQ = 0 - P V^? = constant

45. Invariant Energy Quantity
Z²/n² (m_red/m_elec)
E²-p²c²
X_L = X_C or X_total = 0
I = V/R exp(-t/RC)

46. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
? = h/mv
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
ma + kx = 0

47. Lagrangian and Lagrange'S equation
Hbar*?³/(p²c³exp(hbar?/t)-1)
Measurements close to mean
J = E s - s = Conductivity - E = Electric field
L = T - V dL/dq = d/dt dL/dqdot

48. Atom: Orbital Config
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
P1V1 - P2V2 / (? - 1)
L = T - V dL/dq = d/dt dL/dqdot
Z²/n² (m_red/m_elec)

49. EM: SHO (Hooke)
?= h/v(2mE)
A[B -C] + [A -C]B
J = E s - s = Conductivity - E = Electric field
ma + kx = 0

50. Atom: Positronium Reduced Mass
F = R/2
µ = m_e/2
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.
Measurements close to true value