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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. Atom: Bohr Theory Ionization
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.
E = Z²*E1
? = 5/3
dU = 0 ? dS = ?dW/T

2. Mean electron drift speed
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
<?1|?2> = 0 ? Orthogonal
qvb = mv²/R
J/(ne) n: atom density

3. De Broglie wavelength
U - ts = -tlog(Z)
Z²/n² (m_red/m_elec)
? = h/p
? = ?0 root((1-v/c)/(1+v/c))

4. Adiabatic means
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Isentropic
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
DW/dq

5. Relativistic length contraction
J = ? Fdt
L = L_0 Sqrt[1-v^2/c^2]
µ = m_e/2
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

6. Self Inductance
Const: 2t = (n +.5)? Destructive 2t = n?
V = -L di/dt
Exp(N(µ-e)/t)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

7. Angular momentum - Central Force Motion
N²/Z (m_elec/m_red)
T^2 = k R^3 - k=constant
Sin(?) = ?/d
L = mr²d?/dt

8. Focal point of mirrror with curvature
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
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Int ( A . dr) = Int ( del x A) dSurface
F = R/2

9. Heat added
I = -(c ?t)^2 + d^2
NC?T
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
0

10. Wein'S displacement law for blackbodies (? and T)
A[B -C] + [A -C]B
?~T
?_max = b/T
? = 1.22? / d

11. Magnetic Field Through Ring
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
U = t^2 d/dt (logZ)
I = I_cm + (1/2)m d^2
µ0 I / 2R

12. Helmholtz Free Energy
? = 1.22? / d
Z²/n² (m_red/m_elec)
? = h/p
U - ts = -tlog(Z)

13. Astro: p-p Chain
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
ih_barL_z
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
4H + 2e- ? He +2? + 6?

14. Relativistic interval (which must remain constant for two events)
X_L = X_C or X_total = 0
<T> = -<V>/2
µ=s^2
I = -(c ?t)^2 + d^2

15. Quant: Orthogonality of States
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
<?1|?2> = 0 ? Orthogonal
µ0 I / 2pR

16. Gibbs Factor
µ0 I / 2R
Exp(N(µ-e)/t)
Const: 2t = (n +.5)? Destructive 2t = n?
Opposing charge induced upon conductor

17. Lab: Precision of Measurements
Measurements close to mean
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
F = -2*m(? x r)
F = qv×B

18. Relativistic Energy
?mc²
µ = Current * Area T = µ x B
DS = 0 - dQ = 0 - P V^? = constant
PdV +dU

19. Single Slit Diffraction Intensity
F = qv×B
I = I_0 Cos[?]^2
I = Im (sinc²(a)) ; a = pai sin(?) / ?
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

20. Induced EMF of solenoid
E = s/e_0
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Faraday/Lenz: current inducted opposes the changing field
N d flux / dt

21. Compton Scattering
B = µ0 I n
?? = h/mc * (1-cos(?))
1/2 CV²
?~T

22. Center of Mass: Kinetic Energy & Angular Momentum
F = qv×B
µ0 I1I2 / (2pd)
KE = 1/2 * µ (dr/dt)² L = µ r x v
I = -(c ?t)^2 + d^2

23. Energy in terms of partition function
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
U = t^2 d/dt (logZ)
µ0 I / 2R
?mv

24. Rocket Equation
v(mean)
Z_c = -i/(?C) ; Z_L = i ? L
Dv = -udm/m - v = v0 + u ln(m0/m)
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

25. Quant: Commutator Relation [AB -C]
1/vLC
NC?T
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
A[B -C] + [A -C]B

26. Solid: Resistivity of Metal
X_L = i?L
?~T
.5 LI²
Opposing charge induced upon conductor

27. Magnetic Field For Current in Long Wire
µ0 I / 2pR
<?|O|?>
U - ts = -tlog(Z)
I = I_cm + (1/2)m d^2

28. Rayleigh criterion
?? = h/mc * (1-cos(?))
F = qv×B
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
? = 1.22? / d

29. Partition Function
X_C = 1/(i?C)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
? exp(-e/t)
Int ( A . dr) = Int ( del x A) dSurface

30. EM: Reactance of Inductor
Dp/dt = L / (t ?V)
Cos[?] Sin[?] -Sin[?] Cos[?]
X_L = i?L
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

31. EM: Maxwell'S equations
F = -2*m(? x r)
? = 5/3
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Z_c = -i/(?C) ; Z_L = i ? L

32. EM: Lorentz Force
X_L = i?L
F = qv×B
I = V/R exp(-t/RC)
? = 5/3

33. EM: AC Resonance
µ0 I / 2R
Dp/dt = L / (t ?V)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
X_L = X_C or X_total = 0

34. De Broigle Wavelength
? = h/mv
? = 1.22?/D
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

35. Stark Effect
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
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
? = h/mv
V = -L di/dt

36. Atom: Bohr Formula
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
P/A = s T^4
P² ~ R³
?mc²

37. Pauli matrices
H = H_0 + ?H
Faraday/Lenz: current inducted opposes the changing field
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
Hbar*?³/(p²c³exp(hbar?/t)-1)

38. Quant: Expectation Value
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
<?|O|?>
J/(ne) n: atom density
?_max = b/T

39. Weighted average (mean and unc. of mean)
P/A = s T^4
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
? = 1.22?/D
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

40. Doppler shift for light
S = k ln[O] ; dS = dQ/T
F = R/2
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
L = T - V dL/dq = d/dt dL/dqdot

41. Lab: Accuracy of Measurements
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
?~T
<T> = -<V>/2

42. Rocket Thrust
I = Im (sinc²(a)) ; a = pai sin(?) / ?
P² ~ R³
u dm/dt
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

43. Malus Law

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44. Electromotive Force
DW/dq
? = 5/3
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.
ds² = (c*dt)² - ?(x_i)²

45. Doppler Shift for light
4H + 2e- ? He +2? + 6?
A[B -C] + [A -C]B
? = ?0 root((1-v/c)/(1+v/c))
Cos[?] Sin[?] -Sin[?] Cos[?]

46. Hall Coefficient
1/ne - where n is charge carrier density
E = <?| H |?>
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
.5 LI²

47. Mech: Force of Friction
<T> = -<V>/2
? = h/p
0
F_f = µ*F_N

48. Kepler'S Three Laws
I = V/R exp(-t/RC)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
KE = 1/2 * µ (dr/dt)² L = µ r x v
P +1/2 ? v² + ?gh = Constant

49. Source-free RC Circuit
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
DS = 0 - dQ = 0 - P V^? = constant
<?1|?2> = 0 ? Orthogonal

50. E field of a capacitor (d->0)
F = qv×B
4H + 2e- ? He +2? + 6?
E = s/e_0
V = V0 + V0 a ?T