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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. EM: Series Capacitance
C_eq = (? 1/C_i)^-1
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
I_z = I_x + I_y (think hoop symmetry)
B = µ0 I n

2. Astro: Kepler'S Third Law
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
?mc²
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
P² ~ R³

3. Energy in terms of partition function
J = ? Fdt
V = -L di/dt
?~1/T
U = t^2 d/dt (logZ)

4. Hall Coefficient
?s = 0 - ?l = ±1
I = V/R exp(-t/RC)
1/ne - where n is charge carrier density
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

5. Magnetic Dipole Moment and Torque
P² ~ R³
V(r) + L²2/2mr²
µ = Current * Area T = µ x B
Sin(?) = ?/d

6. Wein'S Displacement Law
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
µ0 I1I2 / (2pd)
?max = 2.898 x 10 -³ / T
V = -L di/dt

7. Thermo: Isothermal
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.
dU = 0 ? dS = ?dW/T
? = 5/3
Sin(?) = ?/d

8. Compton Scattering
X_L = i?L
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
?? = h/mc * (1-cos(?))

9. Helmholtz Free Energy
<?1|?2> = 0 ? Orthogonal
µ0 I1I2 / (2pd)
U - ts = -tlog(Z)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

10. EM: Reactance of Inductor
v(mean)
? = 5/3
DW/dq
X_L = i?L

11. Complex impedance (expressions for capacitor and inductor)
Z_c = -i/(?C) ; Z_L = i ? L
v(mean)
V(r) + L²2/2mr²
F = mv²/r

12. RLC resonance condition
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
<T> = 1/2 * <dV/dx>
?_max = b/T

13. Stefan-Boltzmann law for blackbodies (power per area and T)
P/A = s T^4
Isentropic
? (t-vx/c²)
X_L = i?L

14. 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 = I_cm + (1/2)m d^2
J = ? Fdt
?~1/T

15. Energy in a Capacitor
.5 CV²
ih_barL_z
KE = 1/2 * µ (dr/dt)² L = µ r x v
PdV +dU

16. Single Slit Diffraction Intensity
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
NC?T
T^2 = k R^3 - k=constant
I = Im (sinc²(a)) ; a = pai sin(?) / ?

17. Astro: p-p Chain
Int ( A . dr) = Int ( del x A) dSurface
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
4H + 2e- ? He +2? + 6?
F_f = µ*F_N

18. Pauli matrices
E = s/e_0
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
I = V/R exp(-t/RC)
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

19. Radiation (Larmor - and another neat fact)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
?? = h/mc * (1-cos(?))
0

20. Time Lorentz Transformation
Opposing charge induced upon conductor
Isentropic
P² ~ R³
? (t-vx/c²)

21. Entropy (# of states - and in terms of other thermo quantities)
v(mean)
Measurements close to mean
.5 CV²
S = k ln[O] ; dS = dQ/T

22. Commutator identities ( [B -A C] - [A -B] )
B = µ0 I n
N d flux / dt
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

23. Spherical Capacitor Equation
I = Im (sinc²(a)) ; a = pai sin(?) / ?
C = 4pe0 ab/(a-b) = inner and outer radii
Z = ?g_i*exp(-E/kT)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

24. Malus Law

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25. QM: de Broglie Wavelength
?= h/v(2mE)
?s = 0 - ?l = ±1
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
dU = 0 ? dS = ?dW/T

26. Angular momentum - Central Force Motion
L = mr²d?/dt
C = 4pe0 ab/(a-b) = inner and outer radii
F = µ0 q v I / 2pr
I = I_0 Cos[?]^2

27. A reversible process stays..
ma + kx = 0
Hbar*?³/(p²c³exp(hbar?/t)-1)
Infinitely close to equilibrium at all times
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

28. Boltzmann / Canonical distribution
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Z = ?g_i*exp(-E/kT)
Ct²-x²-y²-z²
Dp/dt = L / (t ?V)

29. Bragg'S Law of Reflection
<?|O|?>
C_eq = ?C_i
M? = 2dsin(?)
(° of Freedom)kT/2

30. Source Free RL Circuit
NC?T
Z = ?g_i*exp(-E/kT)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
qvb = mv²/R

31. Atom: Bohr Formula
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Z²/n² (m_red/m_elec)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

32. Lensmaker Equation - Thin Lens
µ=s^2
V = V0 + V0 a ?T
A[B -C] + [A -C]B
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

33. Self Inductance
F = -2*m(? x r)
1/2 CV²
V = -L di/dt
I = V/R exp(-t/RC)

34. SR: Spacetime Interval
ds² = (c*dt)² - ?(x_i)²
U = t^2 d/dt (logZ)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Hbar*?³/(p²c³exp(hbar?/t)-1)

35. Springs in series/parallel
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
J/(ne) n: atom density

36. Thermo: Average Total Energy
(° of Freedom)kT/2
Dp/dt = L / (t ?V)
Faraday/Lenz: current inducted opposes the changing field
M? = 2dsin(?)

37. Work (P - V)
Infinitely close to equilibrium at all times
P1V1 - P2V2 / (? - 1)
I = I_cm + (1/2)m d^2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

38. 3 Laws of Thermo
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
U = t^2 d/dt (logZ)
?~1/T
Z²/n² (m_red/m_elec)

39. Law of Mass Action
NC?T
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
F = s * T4
C_eq = ?C_i

40. 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)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
DW = P dV
C = 4pe0 ab/(a-b) = inner and outer radii

41. Perpendicular axis theorem
I_z = I_x + I_y (think hoop symmetry)
µ = Current * Area T = µ x B
I = I_cm + (1/2)m d^2
L = mr²d?/dt

42. Biot-Savart law
dU = 0 ? dS = ?dW/T
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
J = E s - s = Conductivity - E = Electric field
I = I_0 Cos[?]^2

43. Thin Film Theory: Constructive / Destructive Interference
?mv
I = I_0 Cos[?]^2
N d flux / dt
Const: 2t = (n +.5)? Destructive 2t = n?

44. Perturbations
?s = 0 - ?l = ±1
Asin(?) = m?
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
H = H_0 + ?H

45. Atom: Positronium Reduced Mass
F = f* (c+v_r)/(c+v_s)
µ = m_e/2
T = I?²/2
Sin(?) = ?/d

46. Atom: Orbital Config
µ = m_e/2
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Always Real
Braking Radiation

47. Polarizers - intensity when crossed at ?
Measurements close to true value
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
µ = m_e/2
I = I_0 Cos[?]^2

48. EM: SHO (Hooke)
F_f = µ*F_N
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
ma + kx = 0
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

49. Thermo: Partition Function
F = f* (c+v_r)/(c+v_s)
E = <?| H |?>
Z = ?g_i*exp(-E/kT)
N²/Z (m_elec/m_red)

50. Selection rules for atomic transitions
? = 1.22?/D
Ct²-x²-y²-z²
µ0 I1I2 / (2pd)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)