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GRE Physics

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Answer 50 questions in 15 minutes.
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1. Doppler Shift in Frequency
I = I_0 Cos[?]^2
I = -(c ?t)^2 + d^2
? = 5/3
F = f* (c+v_r)/(c+v_s)

2. Thermo: Partition Function
Z = ?g_i*exp(-E/kT)
Q = CVexp(-t/RC)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
C = 4pe0 ab/(a-b) = inner and outer radii

3. Energy in Inductor
V(r) + L²2/2mr²
S = k ln[O] ; dS = dQ/T
KE = 1/2 * µ (dr/dt)² L = µ r x v
.5 LI²

4. Commutator identities ( [B -A C] - [A -B] )
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_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)
V = -L di/dt
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

5. Pauli matrices
NC?T
(3/2) n R ?t
dU = 0 ? dS = ?dW/T
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

6. Adiabatic processes (dS - dQ - P and V)
DS = 0 - dQ = 0 - P V^? = constant
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Dp/dt = L / (t ?V)
? = 5/3

7. Malus Law

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8. Kepler'S Three Laws
I = I_0 Cos[?]^2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
DW/dq
KE = 1/2 * µ (dr/dt)² L = µ r x v

9. EM: Reactance of Capacitor
DS = 0 - dQ = 0 - P V^? = constant
X_C = 1/(i?C)
I = I_cm + md²
?? = h/mc * (1-cos(?))

10. Rayleigh criterion
?mv
(° of Freedom)kT/2
? = 1.22? / d
? (t-vx/c²)

11. Lab: Standard Deviation of Poisson
P +1/2 ? v² + ?gh = Constant
T = I?²/2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
v(mean)

12. Mech: Virial Theorem
<T> = -<V>/2
X_L = i?L
?max = 2.898 x 10 -³ / T
Asin(?) = m?

13. Atom: Hydrogen Wave Function Type
µ = m_e/2
F = qv×B
Exponentially decreasing radial function
? = h/p

14. Dulong Petit Law
Cv = dE/dT = 3R
S = k ln[O] ; dS = dQ/T
J/(ne) n: atom density
?~T

15. Astro: p-p Chain
4H + 2e- ? He +2? + 6?
N d flux / dt
J = ? Fdt
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

16. Time Lorentz Transformation
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
U = t^2 d/dt (logZ)
X_L = X_C or X_total = 0
? (t-vx/c²)

17. Quant: Expectation Value
J = ? Fdt
µ0 I / 2R
Exp(N(µ-e)/t)
<?|O|?>

18. Current in resistor in RC circuit
(3/2) n R ?t
I = V/R exp(-t/RC)
B = µ0 I n
C = 4pe0 ab/(a-b) = inner and outer radii

19. Rotation matrix (2x2)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
ds² = (c*dt)² - ?(x_i)²
Cos[?] Sin[?] -Sin[?] Cos[?]
Measurements close to mean

20. Thermo: Monatomic gas ?=?
1/2 CV²
? = 5/3
<T> = 1/2 * <dV/dx>
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

21. Inductance of Solenoid
Const: 2t = (n +.5)? Destructive 2t = n?
F = µ0 q v I / 2pr
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
I ' = I cos²(?)

22. EM: Lorentz Force
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 = qv×B
KE = 1/2 * µ (dr/dt)² L = µ r x v
?s = 0 - ?l = ±1

23. Addition of relativistic velocities

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24. Magnetic Field For Current in Long Wire
F = mv²/r
<T> = -<V>/2
µ0 I / 2pR
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

25. Relativistic length contraction
L = L_0 Sqrt[1-v^2/c^2]
Exp(N(µ-e)/t)
µ=s^2
C = 4pe0 ab/(a-b) = inner and outer radii

26. Mech: Centripetal Force
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
? = 1.22?/D
Braking Radiation
F = mv²/r

27. Complex impedance (expressions for capacitor and inductor)
S = k ln[O] ; dS = dQ/T
Isentropic
I = I_cm + (1/2)m d^2
Z_c = -i/(?C) ; Z_L = i ? L

28. Coriolis Force
P1V1 - P2V2 / (? - 1)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
.5 CV²
F = -2*m(? x r)

29. 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.
I = -(c ?t)^2 + d^2
F_f = µ*F_N
P/A = s T^4

30. Doppler Shift for light
E = s/e_0
? = ?0 root((1-v/c)/(1+v/c))
ds² = (c*dt)² - ?(x_i)²
?s = 0 - ?l = ±1

31. Hall Coefficient
?max = 2.898 x 10 -³ / T
1/ne - where n is charge carrier density
KE = 1/2 * µ (dr/dt)² L = µ r x v
H = H_0 + ?H

32. Planck Radiation Law
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
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>
Hbar*?³/(p²c³exp(hbar?/t)-1)

33. Force exerted on charge by long wire
F = µ0 q v I / 2pr
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
<T> = -<V>/2
C = 4pe0 ab/(a-b) = inner and outer radii

34. Perpendicular axis theorem
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
I_z = I_x + I_y (think hoop symmetry)
W_A < W_I
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

35. Polarizers - intensity when crossed at ?
(° of Freedom)kT/2
I = I_0 Cos[?]^2
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
I = V/R exp(-t/RC)

36. Spherical Capacitor Equation
C = 4pe0 ab/(a-b) = inner and outer radii
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
W_A < W_I
V = V0 + V0 a ?T

37. Atom: Orbital Config
? = 1.22? / d
L = mr²d?/dt
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
ma + kx = 0

38. EM: SHO (Hooke)
?~1/T
ma + kx = 0
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
? = h/p

39. Adiabatic means
u dm/dt
(° of Freedom)kT/2
Isentropic
?max = 2.898 x 10 -³ / T

40. Astro: Kepler'S Third Law
P² ~ R³
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
µ=s^2
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

41. Atom: Bohr Formula
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
U = t^2 d/dt (logZ)
E²-p²c²
B = µ0 I n

42. Poisson distribution (µ and s)
Int ( A . dr) = Int ( del x A) dSurface
I = Im (sinc²(a)) ; a = pai sin(?) / ?
µ=s^2
.5 LI²

43. Magnetic Dipole Moment and Torque
µ = Current * Area T = µ x B
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
0
Exponentially decreasing radial function

44. td(entropy) =
?= h/v(2mE)
? = h/p
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
PdV +dU

45. 3 Laws of Thermo
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
NC?T
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

46. Work in a capacitor
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
1/2 CV²
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
I ' = I cos²(?)

47. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
J = E s - s = Conductivity - E = Electric field
4H + 2e- ? He +2? + 6?
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

48. Anomalous Zeeman Effect

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49. Volumetric Expansion
? exp(-e/t)
V = V0 + V0 a ?T
P +1/2 ? v² + ?gh = Constant
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

50. Single Slit Diffraction Intensity
? = h/mv
T^2 = k R^3 - k=constant
4H + 2e- ? He +2? + 6?
I = Im (sinc²(a)) ; a = pai sin(?) / ?

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