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GRE Physics

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Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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1. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
? = ?0 root((1-v/c)/(1+v/c))
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Int ( A . dr) = Int ( del x A) dSurface

2. Atom: Positronium Reduced Mass
(° of Freedom)kT/2
µ = m_e/2
I = I_0 Cos[?]^2
F = R/2

3. Self Inductance
I = I_cm + md²
P² ~ R³
V = -L di/dt
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

4. QM: de Broglie Wavelength
?= h/v(2mE)
E = <?| H |?>
P² ~ R³
Int ( A . dr) = Int ( del x A) dSurface

5. Astro: Aperture Formula (Rayleigh Criterion)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
? (t-vx/c²)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
? = 1.22?/D

6. Resistance - length - area - rho
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
? (t-vx/c²)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

7. Dulong Petit Law
A[B -C] + [A -C]B
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
?_max = b/T
Cv = dE/dT = 3R

8. Wein'S Displacement Law
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
µ=s^2
?max = 2.898 x 10 -³ / T
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

9. EM: Reactance of Capacitor
?_max = b/T
X_C = 1/(i?C)
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
? exp(-e/t)

10. Bohr Model: Energy
Z²/n² (m_red/m_elec)
Cv = dE/dT = 3R
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

11. 3 Laws of Thermo
µ0 I / 2pR
U - ts = -tlog(Z)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

12. Quant: Eigenvalue of Hermitian Operator
? = 5/3
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Always Real

13. Doppler shift for light
F = qv×B
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
?max = 2.898 x 10 -³ / T

14. Poisson distribution (µ and s)
X_C = 1/(i?C)
Cv = dE/dT = 3R
µ=s^2
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

15. First law of thermodynamics (explain direction of energy for each term)
L = L_0 Sqrt[1-v^2/c^2]
Faraday/Lenz: current inducted opposes the changing field
E = Z²*E1
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

16. Boltzmann / Canonical distribution
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
P/A = s T^4
J = ? Fdt
Const: 2t = (n +.5)? Destructive 2t = n?

17. Solid: Resistivity of Semi-Conductor
?~1/T
J/(ne) n: atom density
I = I_0 Cos[?]^2
µ = m_e/2

18. Center of Mass: Kinetic Energy & Angular Momentum
Braking Radiation
I = Im (sinc²(a)) ; a = pai sin(?) / ?
KE = 1/2 * µ (dr/dt)² L = µ r x v
Hbar*?³/(p²c³exp(hbar?/t)-1)

19. Atom: Hydrogen Wave Function Type
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Exponentially decreasing radial function
Const: 2t = (n +.5)? Destructive 2t = n?
Sin(?) = ?/d

20. Adiabatic processes (dS - dQ - P and V)
qvb = mv²/R
T^2 = k R^3 - k=constant
DS = 0 - dQ = 0 - P V^? = constant
I = I_cm + (1/2)m d^2

21. Thermo: Monatomic gas ?=?
KE = 1/2 * µ (dr/dt)² L = µ r x v
J = E s - s = Conductivity - E = Electric field
I_z = I_x + I_y (think hoop symmetry)
? = 5/3

22. Magnetic Field Through Ring
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
F = -2*m(? x r)
µ0 I / 2R
µ=s^2

23. Virial Theorem
V = -L di/dt
Int ( A . dr) = Int ( del x A) dSurface
<T> = 1/2 * <dV/dx>
ma + kx = 0

24. Weighted average (mean and unc. of mean)
? = ?0 root((1-v/c)/(1+v/c))
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
F = qv×B

25. Commutator identities ( [B -A C] - [A -B] )
T^2 = k R^3 - k=constant
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Dp/dt = L / (t ?V)

26. Stoke'S Theorem
Int ( A . dr) = Int ( del x A) dSurface
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
dU = 0 ? dS = ?dW/T
?mv

27. De Broigle Wavelength
? = h/mv
F = I L X B
? = 1.22?/D
Always Real

28. Rocket Equation
Z_c = -i/(?C) ; Z_L = i ? L
I = V/R exp(-t/RC)
dU = 0 ? dS = ?dW/T
Dv = -udm/m - v = v0 + u ln(m0/m)

29. Compton Scattering
1/ne - where n is charge carrier density
?? = h/mc * (1-cos(?))
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

30. Thermo: Blackbody Radiation
F = s * T4
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
v(mean)
µ = Current * Area T = µ x B

31. Adiabatic means
1/ne - where n is charge carrier density
Const: 2t = (n +.5)? Destructive 2t = n?
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Isentropic

32. Rotation matrix (2x2)
Cos[?] Sin[?] -Sin[?] Cos[?]
B = µ0 I n
C_eq = (? 1/C_i)^-1
L = T - V dL/dq = d/dt dL/dqdot

33. A reversible process stays..
ma + kx = 0
Q = CVexp(-t/RC)
N d flux / dt
Infinitely close to equilibrium at all times

34. Relativistic Momentum
.5 LI²
E²-p²c²
T = I?²/2
?mv

35. 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.
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
W_A < W_I
1/2 CV²

36. Thin Film Theory: Constructive / Destructive Interference
F = I L X B
Const: 2t = (n +.5)? Destructive 2t = n?
L = T - V dL/dq = d/dt dL/dqdot
F = s * T4

37. Mech: Impulse
J = ? Fdt
PdV +dU
Dv = -udm/m - v = v0 + u ln(m0/m)
<?1|?2> = 0 ? Orthogonal

38. Perpendicular axis theorem
I_z = I_x + I_y (think hoop symmetry)
Measurements close to mean
qvb = mv²/R
X_C = 1/(i?C)

39. Quant: Expectation Value
qvb = mv²/R
L = mr²d?/dt
<T> = 1/2 * <dV/dx>
<?|O|?>

40. Atom: Orbital Config
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
I = Im (sinc²(a)) ; a = pai sin(?) / ?
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
I_z = I_x + I_y (think hoop symmetry)

41. Electromotive Force
P² ~ R³
DW/dq
0
Dv = -udm/m - v = v0 + u ln(m0/m)

42. Selection rules for atomic transitions
E = Z²*E1
P1V1 - P2V2 / (? - 1)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
?~1/T

43. Thermo: Average Total Energy
I ' = I cos²(?)
(° of Freedom)kT/2
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

44. Force on a wire in magnetic field
?mc²
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
0
F = I L X B

45. Ohm'S Law w/ current density
<?1|?2> = 0 ? Orthogonal
? = 1.22? / d
J = E s - s = Conductivity - E = Electric field
I = I_0 Cos[?]^2

46. Kepler'S Three Laws
L = T - V dL/dq = d/dt dL/dqdot
I = I_0 Cos[?]^2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
DS = 0 - dQ = 0 - P V^? = constant

47. Source Free RL Circuit
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
?~T

48. Mech: Centripetal Force
F = mv²/r
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
P1V1 - P2V2 / (? - 1)
DW = P dV

49. Mech: Force of Friction
Dp/dt = L / (t ?V)
u dm/dt
F_f = µ*F_N
DW/dq

50. Energy in Inductor
.5 LI²
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
I = I_cm + (1/2)m d^2
N²/Z (m_elec/m_red)

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