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GRE Physics

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1. Solid: Resistivity of Semi-Conductor
u dm/dt
?~1/T
Z_c = -i/(?C) ; Z_L = i ? L
Int ( A . dr) = Int ( del x A) dSurface

2. Energy in Inductor
Ct²-x²-y²-z²
I = V/R exp(-t/RC)
.5 LI²
V(r) + L²2/2mr²

3. 3 Laws of Thermo
Z²/n² (m_red/m_elec)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
PdV +dU
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

4. Energy in a Capacitor
.5 CV²
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.
F = R/2
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

5. Lab: Accuracy of Measurements
Measurements close to true value
M? = 2dsin(?)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
1/2 CV²

6. EM: SHO (Hooke)
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.
qvb = mv²/R
Dp/dt = L / (t ?V)
ma + kx = 0

7. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
4H + 2e- ? He +2? + 6?
I = -(c ?t)^2 + d^2
Braking Radiation

8. Rocket Thrust
u dm/dt
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
?~1/T

9. Bohr Model: Energy
C_eq = ?C_i
Z²/n² (m_red/m_elec)
F = R/2
C_eq = (? 1/C_i)^-1

10. EM: Reactance of Inductor
X_L = i?L
V(r) + L²2/2mr²
ds² = (c*dt)² - ?(x_i)²
E = s/e_0

11. Angular momentum - Central Force Motion
A[B -C] + [A -C]B
?s = 0 - ?l = ±1
µ0 I / 2R
L = mr²d?/dt

12. Hamiltonian and Hamilton'S equations
KE = 1/2 * µ (dr/dt)² L = µ r x v
E = Z²*E1
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Exponentially decreasing radial function

13. Commutator identities ( [B -A C] - [A -B] )
1/vLC
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Z_c = -i/(?C) ; Z_L = i ? L
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

14. Thin Film Theory: Constructive / Destructive Interference
ma + kx = 0
Const: 2t = (n +.5)? Destructive 2t = n?
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Exp(N(µ-e)/t)

15. De Broigle Wavelength
<?|O|?>
? = h/mv
.5 CV²
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

16. Relativistic length contraction
T^2 = k R^3 - k=constant
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
1/vLC
L = L_0 Sqrt[1-v^2/c^2]

17. Astro: Kepler'S Third Law
?~1/T
Const: 2t = (n +.5)? Destructive 2t = n?
F = mv²/r
P² ~ R³

18. Atom: Orbital Config
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
KE = 1/2 * µ (dr/dt)² L = µ r x v
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Z²/n² (m_red/m_elec)

19. EM: Method of Images
C_eq = ?C_i
Opposing charge induced upon conductor
qvb = mv²/R
H = H_0 + ?H

20. Mech: Centripetal Force
F = mv²/r
J = ? Fdt
V = V0 + V0 a ?T
I = V/R exp(-t/RC)

21. QM: de Broglie Wavelength
?= h/v(2mE)
Const: 2t = (n +.5)? Destructive 2t = n?
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
P² ~ R³

22. Work in a capacitor
Infinitely close to equilibrium at all times
?~1/T
1/2 CV²
I = V/R exp(-t/RC)

23. Force on a wire in magnetic field
F = I L X B
Const: 2t = (n +.5)? Destructive 2t = n?
? = 1.22? / d
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

24. Selection rules for atomic transitions
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
DW = P dV
F = f* (c+v_r)/(c+v_s)
P² ~ R³

25. Thermo: Partition Function
DW = P dV
Z = ?g_i*exp(-E/kT)
F = µ0 q v I / 2pr
ma + kx = 0

26. Invariant spatial quantity
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
V(r) + L²2/2mr²
Ct²-x²-y²-z²
Dp/dt = L / (t ?V)

27. Stoke'S Theorem
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
<?1|?2> = 0 ? Orthogonal
I ' = I cos²(?)
Int ( A . dr) = Int ( del x A) dSurface

28. Center of Mass: Kinetic Energy & Angular Momentum
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
KE = 1/2 * µ (dr/dt)² L = µ r x v
<?1|?2> = 0 ? Orthogonal
V(r) + L²2/2mr²

29. Rayleigh'S Criterion
A[B -C] + [A -C]B
P² ~ R³
Sin(?) = ?/d
Z_c = -i/(?C) ; Z_L = i ? L

30. Atom: Positronium Reduced Mass
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
P1V1 - P2V2 / (? - 1)
µ = m_e/2
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

31. Magnetic Dipole Moment and Torque
?max = 2.898 x 10 -³ / T
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
qvb = mv²/R
µ = Current * Area T = µ x B

32. Thermo: Average Total Energy
Always Real
(° of Freedom)kT/2
<T> = -<V>/2
Int ( A . dr) = Int ( del x A) dSurface

33. RLC resonance condition
0
µ0 I / 2R
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

34. Effective Potential
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
V(r) + L²2/2mr²
F = mv²/r
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

35. Single Slit Diffraction Intensity
I = Im (sinc²(a)) ; a = pai sin(?) / ?
(° of Freedom)kT/2
DS = 0 - dQ = 0 - P V^? = constant
? (t-vx/c²)

36. Gibbs Factor
I = V/R exp(-t/RC)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
L = T - V dL/dq = d/dt dL/dqdot
Exp(N(µ-e)/t)

37. Quant: [L_x -L_y] = ?
PdV +dU
F = s * T4
ih_barL_z
Faraday/Lenz: current inducted opposes the changing field

38. Electromotive Force
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
DW/dq

39. A reversible process stays..
Infinitely close to equilibrium at all times
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
µ0 I / 2pR
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

40. Work (P - V)
P1V1 - P2V2 / (? - 1)
µ0 I / 2R
1/vLC
I = -(c ?t)^2 + d^2

41. Addition of relativistic velocities

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42. Planck Radiation Law
Hbar*?³/(p²c³exp(hbar?/t)-1)
T = I?²/2
P² ~ R³
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

43. Lensmaker Equation - Thin Lens
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
? exp(-e/t)
J/(ne) n: atom density

44. Work done on a gas
Always Real
DW = P dV
PdV +dU
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

45. Mech: Parallel Axis Theorem (Moment of Inertia)
<?|O|?>
I ' = I cos²(?)
N²/Z (m_elec/m_red)
I = I_cm + md²

46. Doppler Shift in Frequency
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
F = f* (c+v_r)/(c+v_s)
F = mv²/r
I = I_cm + md²

47. Kepler'S Three Laws
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
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
T = I?²/2
J = E s - s = Conductivity - E = Electric field

48. Quant: Commutator Relation [AB -C]
A[B -C] + [A -C]B
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
J = E s - s = Conductivity - E = Electric field
Z = ?g_i*exp(-E/kT)

49. Selection Rules
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
E = s/e_0
F = qv×B
?s = 0 - ?l = ±1

50. Double Slit: Interference Minimum - Diffraction Minimum
<?|O|?>
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
E = s/e_0

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