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GRE Physics

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Answer 50 questions in 15 minutes.
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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. Quant: Orthogonality of States
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Dp/dt = L / (t ?V)
<?1|?2> = 0 ? Orthogonal

2. Wein'S displacement law for blackbodies (? and T)
?_max = b/T
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.
?s = 0 - ?l = ±1
?= h/v(2mE)

3. De Broglie wavelength
?mc²
? = h/p
KE = 1/2 * µ (dr/dt)² L = µ r x v
Opposing charge induced upon conductor

4. Adiabatic processes (dS - dQ - P and V)
V = -L di/dt
J = ? Fdt
Dp/dt = L / (t ?V)
DS = 0 - dQ = 0 - P V^? = constant

5. Center of Mass: Kinetic Energy & Angular Momentum
F = -2*m(? x r)
NC?T
KE = 1/2 * µ (dr/dt)² L = µ r x v
Cv = dE/dT = 3R

6. Source-free RC Circuit
µ=s^2
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
? = 5/3

7. Focal point of mirrror with curvature
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Ct²-x²-y²-z²
F = R/2
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

8. EM: Lorentz Force
ih_barL_z
F = qv×B
Isentropic
.5 LI²

9. Complex impedance (expressions for capacitor and inductor)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Z_c = -i/(?C) ; Z_L = i ? L
? (t-vx/c²)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

10. Energy in Inductor
L = T - V dL/dq = d/dt dL/dqdot
F = qv×B
.5 LI²
PdV +dU

11. Helmholtz Free Energy
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
A[B -C] + [A -C]B
U - ts = -tlog(Z)
1/vLC

12. Gibbs Factor
? = h/mv
?mv
Dv = -udm/m - v = v0 + u ln(m0/m)
Exp(N(µ-e)/t)

13. Thermo: Average Total Energy
Z = ?g_i*exp(-E/kT)
Exponentially decreasing radial function
u dm/dt
(° of Freedom)kT/2

14. Thin Film Theory: Constructive / Destructive Interference
?s = 0 - ?l = ±1
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Const: 2t = (n +.5)? Destructive 2t = n?
Cos[?] Sin[?] -Sin[?] Cos[?]

15. 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.
N²/Z (m_elec/m_red)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
?mv

16. Astro: p-p Chain
DW/dq
X_L = i?L
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
4H + 2e- ? He +2? + 6?

17. Quant: Eigenvalue of Hermitian Operator
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Always Real
I ' = I cos²(?)
F = qv×B

18. Clausius-Clapeyron Equation
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Isentropic
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Dp/dt = L / (t ?V)

19. Rayleigh criterion
I = I_cm + (1/2)m d^2
? = 1.22? / d
X_C = 1/(i?C)
µ = Current * Area T = µ x B

20. Effective Potential
H = H_0 + ?H
V(r) + L²2/2mr²
qvb = mv²/R
Asin(?) = m?

21. Atom: Orbital Config
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
P1V1 - P2V2 / (? - 1)
dQ = dW +dU

22. Force on a wire in magnetic field
Cv = dE/dT = 3R
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
0
F = I L X B

23. De Broigle Wavelength
KE = 1/2 * µ (dr/dt)² L = µ r x v
?_max = b/T
S = k ln[O] ; dS = dQ/T
? = h/mv

24. Rocket Thrust
F = qv×B
.5 CV²
F = R/2
u dm/dt

25. Error in the mean if each measurement has the same uncertainty s
PdV +dU
S_mean = s/Sqrt[N]
Exponentially decreasing radial function
X_C = 1/(i?C)

26. Mech: Force of Friction
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
F_f = µ*F_N
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
NC?T

27. Solid: Resistivity of Semi-Conductor
F = I L X B
?~1/T
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.
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

28. Ohm'S Law w/ current density
X_L = i?L
J = E s - s = Conductivity - E = Electric field
?= h/v(2mE)
L = T - V dL/dq = d/dt dL/dqdot

29. Entropy (# of states - and in terms of other thermo quantities)
S = k ln[O] ; dS = dQ/T
?mv
µ = Current * Area T = µ x B
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

30. Magnetic Field of a long solenoid
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
B = µ0 I n
Exp(N(µ-e)/t)
L = T - V dL/dq = d/dt dL/dqdot

31. RLC resonance condition
µ0 I / 2R
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Cos[?] Sin[?] -Sin[?] Cos[?]

32. SR: Spacetime Interval
ds² = (c*dt)² - ?(x_i)²
I = I_cm + (1/2)m d^2
? = 5/3
(3/2) n R ?t

33. Anomalous Zeeman Effect

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34. 3 Laws of Thermo
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Dp/dt = L / (t ?V)

35. Volumetric Expansion
µ=s^2
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
V = V0 + V0 a ?T

36. E field of a capacitor (d->0)
<?|O|?>
E = s/e_0
Z_c = -i/(?C) ; Z_L = i ? L
Ct²-x²-y²-z²

37. Quant: [L_x -L_y] = ?
ih_barL_z
?_max = b/T
Q = CVexp(-t/RC)
1/2 CV²

38. Work (P - V)
V(r) + L²2/2mr²
T^2 = k R^3 - k=constant
Cv = dE/dT = 3R
P1V1 - P2V2 / (? - 1)

39. How to derive cylcotron frequency
dU = 0 ? dS = ?dW/T
qvb = mv²/R
F = -2*m(? x r)
Cos[?] Sin[?] -Sin[?] Cos[?]

40. Source Free RL Circuit
?? = h/mc * (1-cos(?))
v(mean)
Measurements close to true value
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

41. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
Dp/dt = L / (t ?V)
<?|O|?>
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Const: 2t = (n +.5)? Destructive 2t = n?

42. Astro: Aperture Formula (Rayleigh Criterion)
NC?T
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
?max = 2.898 x 10 -³ / T
? = 1.22?/D

43. Pauli matrices
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_f = µ*F_N
DW = P dV
J = ? Fdt

44. Perturbations
Infinitely close to equilibrium at all times
Always Real
H = H_0 + ?H
qvb = mv²/R

45. Energy levels from the Coulomb potential
I = I_0 Cos[?]^2
Z_c = -i/(?C) ; Z_L = i ? L
ih_barL_z
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

46. Lagrangian and Lagrange'S equation
1/ne - where n is charge carrier density
L = T - V dL/dq = d/dt dL/dqdot
µ0 I / 2pR
J = E s - s = Conductivity - E = Electric field

47. Atom: Hydrogen Wave Function Type
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
? = 5/3
Exponentially decreasing radial function
Q = CVexp(-t/RC)

48. Quant: Commutator Relation [AB -C]
A[B -C] + [A -C]B
?_max = b/T
u dm/dt
X_L = i?L

49. QM: de Broglie Wavelength
N d flux / dt
.5 LI²
? = h/p
?= h/v(2mE)

50. Inductance of Solenoid
NC?T
W_A < W_I
C = 4pe0 ab/(a-b) = inner and outer radii
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

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