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GRE Physics

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Answer 50 questions in 30 minutes.
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1. Partition Function
? exp(-e/t)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Q = CVexp(-t/RC)
PdV +dU

2. Hall Coefficient
1/ne - where n is charge carrier density
(° of Freedom)kT/2
Cv = dE/dT = 3R
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

3. Bernoulli Equation
E²-p²c²
P +1/2 ? v² + ?gh = Constant
Dp/dt = L / (t ?V)
.5 LI²

4. Law of Mass Action
L = L_0 Sqrt[1-v^2/c^2]
E = s/e_0
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

5. Source Free RL Circuit
P +1/2 ? v² + ?gh = Constant
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
A[B -C] + [A -C]B
Hbar*?³/(p²c³exp(hbar?/t)-1)

6. Hamiltonian and Hamilton'S equations
? = ?0 root((1-v/c)/(1+v/c))
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Opposing charge induced upon conductor
1/2 CV²

7. Malus Law

8. EM: Maxwell'S equations
C_eq = ?C_i
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Hbar*?³/(p²c³exp(hbar?/t)-1)
Z_c = -i/(?C) ; Z_L = i ? L

9. Self Inductance
V = -L di/dt
P² ~ R³
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.
? = 1.22?/D

10. Kepler'S third law (T and R)
T^2 = k R^3 - k=constant
ih_barL_z
<?|O|?>
Q = CVexp(-t/RC)

11. Atom: Positronium Reduced Mass
<?1|?2> = 0 ? Orthogonal
µ = m_e/2
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
F_f = µ*F_N

12. Expectation value of the energy of state |?>
J = ? Fdt
F_f = µ*F_N
E = <?| H |?>
X_C = 1/(i?C)

13. Energy in Inductor
.5 LI²
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
? = 1.22? / d
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

14. Helmholtz Free Energy
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
I = I_cm + (1/2)m d^2
J/(ne) n: atom density
U - ts = -tlog(Z)

15. Angular momentum operators L^2 and L_z
M? = 2dsin(?)
u dm/dt
µ=s^2
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

16. Rocket Equation
?= h/v(2mE)
µ0 I / 2pR
Dv = -udm/m - v = v0 + u ln(m0/m)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

17. Complex impedance (expressions for capacitor and inductor)
Z_c = -i/(?C) ; Z_L = i ? L
?mv
? exp(-e/t)
T^2 = k R^3 - k=constant

18. EM: Series Capacitance
DW/dq
C_eq = (? 1/C_i)^-1
Cv = dE/dT = 3R
Int ( A . dr) = Int ( del x A) dSurface

19. Force exerted on charge by long wire
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
S = k ln[O] ; dS = dQ/T
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
F = µ0 q v I / 2pr

20. Rocket Thrust
u dm/dt
Cos[?] Sin[?] -Sin[?] Cos[?]
<?1|?2> = 0 ? Orthogonal
I = I_cm + (1/2)m d^2

21. Focal point of mirrror with curvature
F = R/2
.5 CV²
<?|O|?>
I ' = I cos²(?)

22. Work in a capacitor
1/2 CV²
V = V0 + V0 a ?T
L = T - V dL/dq = d/dt dL/dqdot
Cv = dE/dT = 3R

23. Wein'S displacement law for blackbodies (? and T)
?mc²
?_max = b/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.
Infinitely close to equilibrium at all times

24. Relativistic Energy
Faraday/Lenz: current inducted opposes the changing field
?mc²
Measurements close to mean
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

25. Lab: Accuracy of Measurements
T^2 = k R^3 - k=constant
? = 1.22?/D
4H + 2e- ? He +2? + 6?
Measurements close to true value

26. Stoke'S Theorem
u dm/dt
DW/dq
Int ( A . dr) = Int ( del x A) dSurface
J/(ne) n: atom density

27. Invariant Energy Quantity
C_eq = ?C_i
E²-p²c²
J/(ne) n: atom density
Cv = dE/dT = 3R

28. Doppler Shift for light
Measurements close to mean
Measurements close to true value
? = ?0 root((1-v/c)/(1+v/c))
W_A < W_I

29. QM: de Broglie Wavelength
DW/dq
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
?= h/v(2mE)
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.

30. E field of a capacitor (d->0)
E = s/e_0
F = mv²/r
U - ts = -tlog(Z)
Int ( A . dr) = Int ( del x A) dSurface

31. Lensmaker Equation - Thin Lens
S = k ln[O] ; dS = dQ/T
T = I?²/2
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
ma + kx = 0

32. SR: Total Energy of a Particle
µ0 I / 2pR
1/2 CV²
Measurements close to mean
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

33. How to derive cylcotron frequency
qvb = mv²/R
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
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.
Sin(?) = ?/d

34. Thermo: Adiabatic Work vs Isothermal Work
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
.5 LI²
W_A < W_I
PdV +dU

35. Thermo: 1st Law
Exp(N(µ-e)/t)
?= h/v(2mE)
dQ = dW +dU
Ct²-x²-y²-z²

36. Quant: Orthogonality of States
DS = 0 - dQ = 0 - P V^? = constant
KE = 1/2 * µ (dr/dt)² L = µ r x v
<?1|?2> = 0 ? Orthogonal
PdV +dU

37. Virial Theorem
qvb = mv²/R
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
<T> = 1/2 * <dV/dx>

38. Quant: [L_x -L_y] = ?
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
ih_barL_z
X_L = i?L

39. Parallel axis theorem
I = I_cm + (1/2)m d^2
C = 4pe0 ab/(a-b) = inner and outer radii
Exponentially decreasing radial function
? = ?0 root((1-v/c)/(1+v/c))

40. EM: Method of Images
?~1/T
Opposing charge induced upon conductor
Z²/n² (m_red/m_elec)
<?|O|?>

41. Atom: Bohr Formula
P/A = s T^4
PdV +dU
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

42. EM: Reactance of Inductor
X_L = i?L
?~T
?mv
I ' = I cos²(?)

43. 3 Laws of Thermo
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
P +1/2 ? v² + ?gh = Constant
Exp(N(µ-e)/t)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

44. Bar magnets -- direction of B field lines - earth'S B field
E²-p²c²
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
PdV +dU
F = I L X B

45. Coriolis Force
F = -2*m(? x r)
J/(ne) n: atom density
N²/Z (m_elec/m_red)
Q = CVexp(-t/RC)

46. Astro: p-p Chain
dU = 0 ? dS = ?dW/T
4H + 2e- ? He +2? + 6?
N d flux / dt
<?1|?2> = 0 ? Orthogonal

47. Mean electron drift speed
DW/dq
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
J/(ne) n: atom density
Measurements close to mean

48. Adiabatic processes (dS - dQ - P and V)
Sin(?) = ?/d
U = t^2 d/dt (logZ)
DS = 0 - dQ = 0 - P V^? = constant
?? = h/mc * (1-cos(?))

49. De Broigle Wavelength
Isentropic
I = I_cm + (1/2)m d^2
? = h/mv
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

50. Doppler Shift in Frequency
Z = ?g_i*exp(-E/kT)
(3/2) n R ?t
ds² = (c*dt)² - ?(x_i)²
F = f* (c+v_r)/(c+v_s)

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GRE Physics

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After Effects Keyboard Shortcuts

Agile Development

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Android Programming

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