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GRE Physics

Instructions:

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. Parallel axis theorem
L = T - V dL/dq = d/dt dL/dqdot
I = I_cm + (1/2)m d^2
F = µ0 q v I / 2pr
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

2. Effective Potential
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
V(r) + L²2/2mr²
I = I_0 Cos[?]^2
X_C = 1/(i?C)

3. Energy in a Capacitor
.5 CV²
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
dU = 0 ? dS = ?dW/T
Isentropic

4. Entropy (# of states - and in terms of other thermo quantities)
S = k ln[O] ; dS = dQ/T
T = I?²/2
? = ?0 root((1-v/c)/(1+v/c))
C = 4pe0 ab/(a-b) = inner and outer radii

5. E field of a capacitor (d->0)
ds² = (c*dt)² - ?(x_i)²
Const: 2t = (n +.5)? Destructive 2t = n?
DS = 0 - dQ = 0 - P V^? = constant
E = s/e_0

6. Thermo: Partition Function
Z = ?g_i*exp(-E/kT)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Isentropic
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

7. Bohr Model: Energy
dU = 0 ? dS = ?dW/T
?~T
E²-p²c²
Z²/n² (m_red/m_elec)

8. Adiabatic means
Isentropic
I_z = I_x + I_y (think hoop symmetry)
S = k ln[O] ; dS = dQ/T
P +1/2 ? v² + ?gh = Constant

9. Atom: Bohr Theory Ionization
NC?T
Cos[?] Sin[?] -Sin[?] Cos[?]
E = Z²*E1
<T> = 1/2 * <dV/dx>

10. Heat added
µ=s^2
Isentropic
NC?T
A[B -C] + [A -C]B

11. Quant: [L_x -L_y] = ?
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
DW = P dV
Dp/dt = L / (t ?V)

12. Error in the mean if each measurement has the same uncertainty s
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
F = f* (c+v_r)/(c+v_s)
S_mean = s/Sqrt[N]
V(r) + L²2/2mr²

13. How to derive cylcotron frequency
X_C = 1/(i?C)
qvb = mv²/R
NC?T
P1V1 - P2V2 / (? - 1)

14. Commutator identities ( [B -A C] - [A -B] )
.5 LI²
NC?T
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
0

15. Mech: Virial Theorem
<T> = -<V>/2
µ=s^2
µ0 I / 2R
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

16. Lab: Precision of Measurements
X_L = X_C or X_total = 0
Measurements close to mean
I = I_0 Cos[?]^2
?? = h/mc * (1-cos(?))

17. Thermo: 1st Law
U = t^2 d/dt (logZ)
dQ = dW +dU
? = h/p
F = I L X B

18. EM: Electromagnetic inertia
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
X_L = i?L
J = ? Fdt
Faraday/Lenz: current inducted opposes the changing field

19. Selection rules for atomic transitions
?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>
T^2 = k R^3 - k=constant
S = k ln[O] ; dS = dQ/T

20. Compton Scattering
?? = h/mc * (1-cos(?))
Sin(?) = ?/d
N d flux / dt
µ0 I1I2 / (2pd)

21. Weighted average (mean and unc. of mean)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Braking Radiation
KE = 1/2 * µ (dr/dt)² L = µ r x v
Asin(?) = m?

22. Energy in Inductor
.5 LI²
Cv = dE/dT = 3R
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
M? = 2dsin(?)

23. Gibbs Factor
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Exp(N(µ-e)/t)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
C_eq = (? 1/C_i)^-1

24. EM: SHO (Hooke)
B = µ0 I n
H = H_0 + ?H
E = Z²*E1
ma + kx = 0

25. EM: Reactance of Inductor
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
X_L = i?L
I = I_0 Cos[?]^2
Sin(?) = ?/d

26. Expectation value of the energy of state |?>
V = V0 + V0 a ?T
E = <?| H |?>
(° of Freedom)kT/2
X_L = X_C or X_total = 0

27. Mean electron drift speed
J/(ne) n: atom density
1/vLC
Asin(?) = m?
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

28. EM: Lorentz Force
Asin(?) = m?
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
E = Z²*E1
F = qv×B

29. Spherical Capacitor Equation
(° of Freedom)kT/2
C = 4pe0 ab/(a-b) = inner and outer radii
Hbar*?³/(p²c³exp(hbar?/t)-1)
F = f* (c+v_r)/(c+v_s)

30. Relativistic length contraction
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Ct²-x²-y²-z²
v(mean)
L = L_0 Sqrt[1-v^2/c^2]

31. Lensmaker Equation - Thin Lens
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
P/A = s T^4
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

32. Perpendicular axis theorem
I_z = I_x + I_y (think hoop symmetry)
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
J/(ne) n: atom density
1/2 CV²

33. Boltzmann / Canonical distribution
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
F = s * T4
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
T = I?²/2

34. Magnetic Field of a long solenoid
B = µ0 I n
? = ?0 root((1-v/c)/(1+v/c))
L = mr²d?/dt
Infinitely close to equilibrium at all times

35. Internal Energy of an Ideal Gas
C = 4pe0 ab/(a-b) = inner and outer radii
(3/2) n R ?t
?mv
<?|O|?>

36. Lagrangian and Lagrange'S equation
L = T - V dL/dq = d/dt dL/dqdot
T^2 = k R^3 - k=constant
Const: 2t = (n +.5)? Destructive 2t = n?
Hbar*?³/(p²c³exp(hbar?/t)-1)

37. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
N d flux / dt
F = mv²/r
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

38. Stefan-Boltzmann law for blackbodies (power per area and T)
NC?T
ma + kx = 0
P/A = s T^4
N²/Z (m_elec/m_red)

39. Selection Rules
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
X_L = i?L
B = µ0 I n
?s = 0 - ?l = ±1

40. Quant: Commutator Relation [AB -C]
H = H_0 + ?H
1/ne - where n is charge carrier density
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
A[B -C] + [A -C]B

41. Atom: Bohr Formula
C = 4pe0 ab/(a-b) = inner and outer radii
Infinitely close to equilibrium at all times
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Hbar*?³/(p²c³exp(hbar?/t)-1)

42. Partition Function
? exp(-e/t)
DW = P dV
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
J = ? Fdt

43. Force on a wire in magnetic field
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
X_C = 1/(i?C)
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 = I L X B

44. De Broigle Wavelength
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
? = h/mv
L = mr²d?/dt
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

45. Atom: Hydrogen Wave Function Type
Exponentially decreasing radial function
?= h/v(2mE)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

46. Source-free RC Circuit
T^2 = k R^3 - k=constant
PdV +dU
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Infinitely close to equilibrium at all times

47. Springs in series/parallel
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 = f* (c+v_r)/(c+v_s)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
C_eq = (? 1/C_i)^-1

48. Astro: p-p Chain
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
? = h/p
A[B -C] + [A -C]B
4H + 2e- ? He +2? + 6?

49. Thermo: Isothermal
dU = 0 ? dS = ?dW/T
NC?T
V = -L di/dt
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

50. EM: Method of Images
?s = 0 - ?l = ±1
Opposing charge induced upon conductor
dQ = dW +dU
?L/A - L = length - A = cross sectional area - rho is electrical resistivity