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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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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. Stefan-Boltzmann law for blackbodies (power per area and T)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
P/A = s T^4
Infinitely close to equilibrium at all times
I = I_0 Cos[?]^2

2. Lagrangian and Lagrange'S equation
L = T - V dL/dq = d/dt dL/dqdot
C = 4pe0 ab/(a-b) = inner and outer radii
? = 5/3
I = Im (sinc²(a)) ; a = pai sin(?) / ?

3. Dulong Petit Law
µ0 I / 2R
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
Cv = dE/dT = 3R
u dm/dt

4. Single Slit Diffraction Intensity
E²-p²c²
Infinitely close to equilibrium at all times
X_C = 1/(i?C)
I = Im (sinc²(a)) ; a = pai sin(?) / ?

5. Stark Effect
1/ne - where n is charge carrier density
NC?T
? = 5/3
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

6. Selection rules for atomic transitions
W_A < W_I
(° of Freedom)kT/2
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
µ=s^2

7. EM: Parallel Capacitance
F = s * T4
C_eq = ?C_i
C_eq = (? 1/C_i)^-1
Q = CVexp(-t/RC)

8. Wein'S Displacement Law
1/2 CV²
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
?max = 2.898 x 10 -³ / T
I = Im (sinc²(a)) ; a = pai sin(?) / ?

9. Mech: Centripetal Force
1/ne - where n is charge carrier density
PdV +dU
E = <?| H |?>
F = mv²/r

10. Compton Scattering
? = ?0 root((1-v/c)/(1+v/c))
?? = h/mc * (1-cos(?))
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
F = f* (c+v_r)/(c+v_s)

11. Relativistic Momentum
? = 1.22? / d
?mv
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
.5 CV²

12. Invariant spatial quantity
I = I_cm + (1/2)m d^2
F = mv²/r
Ct²-x²-y²-z²
µ = Current * Area T = µ x B

13. Work (P - V)
Exp(N(µ-e)/t)
I = V/R exp(-t/RC)
H = H_0 + ?H
P1V1 - P2V2 / (? - 1)

14. Force/length between two wires
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
E²-p²c²
µ0 I1I2 / (2pd)
v(mean)

15. Force exerted on charge by long wire
F = f* (c+v_r)/(c+v_s)
Faraday/Lenz: current inducted opposes the changing field
Braking Radiation
F = µ0 q v I / 2pr

16. Poisson distribution (µ and s)
.5 CV²
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
µ=s^2

17. 3 Laws of Thermo
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
P/A = s T^4
Faraday/Lenz: current inducted opposes the changing field
1/ne - where n is charge carrier density

18. Coriolis Force
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Cos[?] Sin[?] -Sin[?] Cos[?]
F = -2*m(? x r)

19. Rocket Thrust
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
u dm/dt
I_z = I_x + I_y (think hoop symmetry)
F = µ0 q v I / 2pr

20. Stoke'S Theorem
<?1|?2> = 0 ? Orthogonal
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
Int ( A . dr) = Int ( del x A) dSurface

21. Bernoulli Equation
P +1/2 ? v² + ?gh = Constant
Isentropic
Opposing charge induced upon conductor
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

22. Adiabatic processes (dS - dQ - P and V)
? = 5/3
0
DS = 0 - dQ = 0 - P V^? = constant
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

23. Quant: Expectation Value
?mc²
<?|O|?>
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
I = V/R exp(-t/RC)

24. Atom: Bohr Formula
I = I_cm + md²
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Dp/dt = L / (t ?V)

25. Source-free RC Circuit
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
(3/2) n R ?t
Sin(?) = ?/d
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

26. Invariant Energy Quantity
ih_barL_z
E²-p²c²
E = s/e_0
1/ne - where n is charge carrier density

27. Thermo: Adiabatic Work vs Isothermal Work
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
F = I L X B
ih_barL_z
W_A < W_I

28. Gibbs Factor
? exp(-e/t)
F = R/2
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Exp(N(µ-e)/t)

29. Biot-Savart law
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
F = I L X B
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
?= h/v(2mE)

30. td(entropy) =
Always Real
PdV +dU
F = R/2
NC?T

31. Energy levels from the Coulomb potential
I_z = I_x + I_y (think hoop symmetry)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
Opposing charge induced upon conductor
F = -2*m(? x r)

32. Thermo: Partition Function
u dm/dt
W_A < W_I
Z = ?g_i*exp(-E/kT)
Const: 2t = (n +.5)? Destructive 2t = n?

33. Source Free RL Circuit
I ' = I cos²(?)
J = E s - s = Conductivity - E = Electric field
F = R/2
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

34. Atom: Orbital Config
v(mean)
X_L = i?L
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
? exp(-e/t)

35. Mech: Force of Friction
Ct²-x²-y²-z²
F_f = µ*F_N
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
? = ?0 root((1-v/c)/(1+v/c))

36. A reversible process stays..
1/vLC
Infinitely close to equilibrium at all times
E = <?| H |?>
dU = 0 ? dS = ?dW/T

37. Relativistic length contraction
Dp/dt = L / (t ?V)
U = t^2 d/dt (logZ)
<?1|?2> = 0 ? Orthogonal
L = L_0 Sqrt[1-v^2/c^2]

38. Heat added
? = 1.22? / d
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Braking Radiation
NC?T

39. First law of thermodynamics (explain direction of energy for each term)
Sin(?) = ?/d
F = s * T4
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Dp/dt = L / (t ?V)

40. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
E = <?| H |?>
Isentropic
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
F = R/2

41. Entropy (# of states - and in terms of other thermo quantities)
C = 4pe0 ab/(a-b) = inner and outer radii
Measurements close to mean
Dp/dt = L / (t ?V)
S = k ln[O] ; dS = dQ/T

42. Spherical Capacitor Equation
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
C = 4pe0 ab/(a-b) = inner and outer radii
F = s * T4
KE = 1/2 * µ (dr/dt)² L = µ r x v

43. Internal Energy of an Ideal Gas
E²-p²c²
(3/2) n R ?t
L = T - V dL/dq = d/dt dL/dqdot
Cos[?] Sin[?] -Sin[?] Cos[?]

44. Helmholtz Free Energy
E = <?| H |?>
X_C = 1/(i?C)
L = T - V dL/dq = d/dt dL/dqdot
U - ts = -tlog(Z)

45. EM: Reactance of Capacitor
?_max = b/T
µ0 I / 2R
X_C = 1/(i?C)
1/2 CV²

46. Double Slit: Interference Minimum - Diffraction Minimum
1/ne - where n is charge carrier density
C = 4pe0 ab/(a-b) = inner and outer radii
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
T^2 = k R^3 - k=constant

47. Kepler'S Three Laws
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
F = s * T4
KE = 1/2 * µ (dr/dt)² L = µ r x v
C_eq = (? 1/C_i)^-1

48. Doppler Shift in Frequency
?mc²
F = -2*m(? x r)
F = f* (c+v_r)/(c+v_s)
?~1/T

49. Resistance - length - area - rho
N d flux / dt
ih_barL_z
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.
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

50. Force on a wire in magnetic field
Q = CVexp(-t/RC)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
F = I L X B
T = I?²/2

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