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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. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
µ0 I / 2pR
L = L_0 Sqrt[1-v^2/c^2]
PdV +dU

2. Polarizers - intensity when crossed at ?
I = I_0 Cos[?]^2
Cv = dE/dT = 3R
<?1|?2> = 0 ? Orthogonal
Sin(?) = ?/d

3. Mech: Centripetal Force
F = mv²/r
<T> = -<V>/2
V = V0 + V0 a ?T
I = Im (sinc²(a)) ; a = pai sin(?) / ?

4. Magnetic Dipole Moment and Torque
µ = Current * Area T = µ x B
F = I L X B
F_f = µ*F_N
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

5. Angular momentum - Central Force Motion
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
L = mr²d?/dt
C_eq = ?C_i
W_A < W_I

6. Triplet/singlet states: symmetry and net spin
? = 5/3
?_max = b/T
ih_barL_z
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

7. Doppler Shift for light
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
? = ?0 root((1-v/c)/(1+v/c))
1/vLC
(3/2) n R ?t

8. Energy in terms of partition function
F = s * T4
N²/Z (m_elec/m_red)
I = I_cm + (1/2)m d^2
U = t^2 d/dt (logZ)

9. Quant: [L_x -L_y] = ?
J = ? Fdt
Asin(?) = m?
E = s/e_0
ih_barL_z

10. EM: Method of Images
S_mean = s/Sqrt[N]
Opposing charge induced upon conductor
F = I L X B
I = Im (sinc²(a)) ; a = pai sin(?) / ?

11. Magnetic Field of a long solenoid
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
?~T
0
B = µ0 I n

12. Stark Effect
? = 1.22?/D
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
X_C = 1/(i?C)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

13. Anomalous Zeeman Effect

14. Planck Radiation Law
Hbar*?³/(p²c³exp(hbar?/t)-1)
?~T
4H + 2e- ? He +2? + 6?
?_max = b/T

15. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Dv = -udm/m - v = v0 + u ln(m0/m)
? = h/p
µ = Current * Area T = µ x B

16. Work in a capacitor
X_L = X_C or X_total = 0
F_f = µ*F_N
1/2 CV²
C_eq = ?C_i

17. Helmholtz Free Energy
V = -L di/dt
dQ = dW +dU
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
U - ts = -tlog(Z)

18. Energy in Inductor
P/A = s T^4
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
.5 LI²
1/ne - where n is charge carrier density

19. A reversible process stays..
Hbar*?³/(p²c³exp(hbar?/t)-1)
Infinitely close to equilibrium at all times
J/(ne) n: atom density
P/A = s T^4

20. Bohr Model: Radii
Always Real
L = T - V dL/dq = d/dt dL/dqdot
N²/Z (m_elec/m_red)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

21. De Broglie wavelength
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
? = h/p
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
T^2 = k R^3 - k=constant

22. Parallel axis theorem
I = I_cm + (1/2)m d^2
P +1/2 ? v² + ?gh = Constant
Cv = dE/dT = 3R
B = µ0 I n

23. Work (P - V)
A[B -C] + [A -C]B
P1V1 - P2V2 / (? - 1)
?max = 2.898 x 10 -³ / T
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

24. Kepler'S Three Laws
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
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
T = I?²/2

25. Relativistic interval (which must remain constant for two events)
Const: 2t = (n +.5)? Destructive 2t = n?
I = V/R exp(-t/RC)
I = -(c ?t)^2 + d^2
E = Z²*E1

26. EM: Reactance of Inductor
?? = h/mc * (1-cos(?))
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
V = V0 + V0 a ?T
X_L = i?L

27. Energy in a Capacitor
Z = ?g_i*exp(-E/kT)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
M? = 2dsin(?)
.5 CV²

28. Rayleigh criterion
T = I?²/2
U = t^2 d/dt (logZ)
? = ?0 root((1-v/c)/(1+v/c))
? = 1.22? / d

29. EM: Electromagnetic inertia
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.
Faraday/Lenz: current inducted opposes the changing field
C = 4pe0 ab/(a-b) = inner and outer radii
.5 CV²

30. Inductance of Solenoid
µ = Current * Area T = µ x B
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
A[B -C] + [A -C]B
E²-p²c²

31. Law of Mass Action
Braking Radiation
ds² = (c*dt)² - ?(x_i)²
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

32. SR: Spacetime Interval
ds² = (c*dt)² - ?(x_i)²
Faraday/Lenz: current inducted opposes the changing field
S = k ln[O] ; dS = dQ/T
?_max = b/T

33. Perturbations
F = R/2
C = 4pe0 ab/(a-b) = inner and outer radii
H = H_0 + ?H
(3/2) n R ?t

34. Addition of relativistic velocities

35. Electromotive Force
DW/dq
Dp/dt = L / (t ?V)
J = E s - s = Conductivity - E = Electric field
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

36. Mech: Parallel Axis Theorem (Moment of Inertia)
U - ts = -tlog(Z)
I = I_cm + md²
Exponentially decreasing radial function
X_L = i?L

37. Solid: Resistivity of Semi-Conductor
dQ = dW +dU
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
B = µ0 I n
?~1/T

38. EM: Lorentz Force
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
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.
Faraday/Lenz: current inducted opposes the changing field
F = qv×B

39. Boltzmann / Canonical distribution
<T> = 1/2 * <dV/dx>
.5 LI²
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

40. Thermo: Partition Function
Z = ?g_i*exp(-E/kT)
ds² = (c*dt)² - ?(x_i)²
?mv
L = T - V dL/dq = d/dt dL/dqdot

41. Self Inductance
V = -L di/dt
Sin(?) = ?/d
F = f* (c+v_r)/(c+v_s)
V = V0 + V0 a ?T

42. EM: Maxwell'S equations
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
U - ts = -tlog(Z)
ds² = (c*dt)² - ?(x_i)²

43. Bohr Model: Energy
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
L = T - V dL/dq = d/dt dL/dqdot
Measurements close to mean
Z²/n² (m_red/m_elec)

44. Wein'S displacement law for blackbodies (? and T)
C = 4pe0 ab/(a-b) = inner and outer radii
ds² = (c*dt)² - ?(x_i)²
?_max = b/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

45. EM: AC Resonance
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
S = k ln[O] ; dS = dQ/T
X_L = X_C or X_total = 0
µ = m_e/2

46. Gibbs Factor
Sin(?) = ?/d
I = I_cm + md²
I ' = I cos²(?)
Exp(N(µ-e)/t)

47. Wein'S Displacement Law
DW/dq
?max = 2.898 x 10 -³ / T
F = qv×B
U - ts = -tlog(Z)

48. Springs in series/parallel
? = h/p
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
?mc²

49. Relativistic Energy
<T> = 1/2 * <dV/dx>
Dp/dt = L / (t ?V)
?mc²
I = -(c ?t)^2 + d^2

50. EM: Bremsstrahlung (translation)
Z_c = -i/(?C) ; Z_L = i ? L
Braking Radiation
(3/2) n R ?t
F = -2*m(? x r)