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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. Electromotive Force
S_mean = s/Sqrt[N]
L = mr²d?/dt
F = I L X B
DW/dq

2. Heat added
U = t^2 d/dt (logZ)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Hbar*?³/(p²c³exp(hbar?/t)-1)
NC?T

3. EM: Electromagnetic inertia
Faraday/Lenz: current inducted opposes the changing field
Braking Radiation
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
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

4. Rocket Thrust
E = Z²*E1
u dm/dt
I = I_cm + md²
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

5. EM: SHO (Hooke)
F = f* (c+v_r)/(c+v_s)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
ma + kx = 0
F = I L X B

6. Ohm'S Law w/ current density
E = Z²*E1
J = E s - s = Conductivity - E = Electric field
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Isentropic

7. Astro: Aperture Formula (Rayleigh Criterion)
? = 1.22?/D
I_z = I_x + I_y (think hoop symmetry)
µ=s^2
Dp/dt = L / (t ?V)

8. Invariant spatial quantity
S = k ln[O] ; dS = dQ/T
Opposing charge induced upon conductor
?? = h/mc * (1-cos(?))
Ct²-x²-y²-z²

9. Commutator identities ( [B -A C] - [A -B] )
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
v(mean)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
F = µ0 q v I / 2pr

10. Effective Potential
H = H_0 + ?H
F_f = µ*F_N
(° of Freedom)kT/2
V(r) + L²2/2mr²

11. Compton Scattering
Opposing charge induced upon conductor
NC?T
µ=s^2
?? = h/mc * (1-cos(?))

12. Adiabatic processes (dS - dQ - P and V)
? exp(-e/t)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
1/ne - where n is charge carrier density
DS = 0 - dQ = 0 - P V^? = constant

13. Perturbations
PdV +dU
X_L = X_C or X_total = 0
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
H = H_0 + ?H

14. Source Free RL Circuit
? = h/p
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
? = 1.22? / d
C = 4pe0 ab/(a-b) = inner and outer radii

15. Law of Mass Action
qvb = mv²/R
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
? = 1.22? / d
Z²/n² (m_red/m_elec)

16. Single Slit Diffraction Maximum
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Always Real
Asin(?) = m?
C_eq = ?C_i

17. Angular momentum operators L^2 and L_z
F = qv×B
N d flux / dt
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
J = E s - s = Conductivity - E = Electric field

18. Addition of relativistic velocities

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19. Quant: Expectation Value
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Const: 2t = (n +.5)? Destructive 2t = n?
<?|O|?>
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

20. Magnetic field due to a segment of wire
Cos[?] Sin[?] -Sin[?] Cos[?]
? = 1.22?/D
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

21. Energy in terms of partition function
T = I?²/2
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
U = t^2 d/dt (logZ)

22. Doppler Shift for light
N²/Z (m_elec/m_red)
Opposing charge induced upon conductor
qvb = mv²/R
? = ?0 root((1-v/c)/(1+v/c))

23. Planck Radiation Law
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Hbar*?³/(p²c³exp(hbar?/t)-1)
PdV +dU
J/(ne) n: atom density

24. Adiabatic means
F_f = µ*F_N
P² ~ R³
Isentropic
P1V1 - P2V2 / (? - 1)

25. De Broigle Wavelength
?mv
Cv = dE/dT = 3R
? = h/mv
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

26. Self Inductance
V = -L di/dt
0
J = ? Fdt
I = -(c ?t)^2 + d^2

27. Relativistic Momentum
1/ne - where n is charge carrier density
?~1/T
W_A < W_I
?mv

28. Force on a wire in magnetic field
F = mv²/r
KE = 1/2 * µ (dr/dt)² L = µ r x v
F = I L X B
0

29. Perpendicular axis theorem
PdV +dU
I_z = I_x + I_y (think hoop symmetry)
DS = 0 - dQ = 0 - P V^? = constant
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

30. E field of a capacitor (d->0)
Braking Radiation
F = I L X B
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
E = s/e_0

31. Magnetic Field For Current in Long Wire
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
I ' = I cos²(?)
µ0 I / 2pR
I = Im (sinc²(a)) ; a = pai sin(?) / ?

32. Hamiltonian and Hamilton'S equations
1/vLC
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

33. Poisson distribution (µ and s)
µ=s^2
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
I = I_0 Cos[?]^2
P +1/2 ? v² + ?gh = Constant

34. Weighted average (mean and unc. of mean)
?? = h/mc * (1-cos(?))
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
S_mean = s/Sqrt[N]
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

35. Atom: Orbital Config
?_max = b/T
E = Z²*E1
? = h/mv
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

36. Quant: Eigenvalue of Hermitian Operator
(° of Freedom)kT/2
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
?mv
Always Real

37. Lab: Precision of Measurements
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Const: 2t = (n +.5)? Destructive 2t = n?
Measurements close to mean
? = 1.22? / d

38. Quant: Commutator Relation [AB -C]
Z_c = -i/(?C) ; Z_L = i ? L
A[B -C] + [A -C]B
µ0 I / 2R
Const: 2t = (n +.5)? Destructive 2t = n?

39. Spherical Capacitor Equation
V = -L di/dt
Braking Radiation
C = 4pe0 ab/(a-b) = inner and outer radii
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

40. Helmholtz Free Energy
Measurements close to true value
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
?s = 0 - ?l = ±1
U - ts = -tlog(Z)

41. Double Slit: Interference Minimum - Diffraction Minimum
Int ( A . dr) = Int ( del x A) dSurface
I = V/R exp(-t/RC)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

42. Magnetic Field Through Ring
µ0 I / 2R
F = I L X B
X_L = X_C or X_total = 0
ma + kx = 0

43. Lensmaker Equation - Thin Lens
J = E s - s = Conductivity - E = Electric field
Sin(?) = ?/d
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
?mc²

44. Force exerted on charge by long wire
E = <?| H |?>
1/2 CV²
?? = h/mc * (1-cos(?))
F = µ0 q v I / 2pr

45. Astro: Kepler'S Third Law
u dm/dt
P² ~ R³
?max = 2.898 x 10 -³ / T
1/vLC

46. Focal point of mirrror with curvature
Infinitely close to equilibrium at all times
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
F = R/2
? = h/p

47. Relativistic interval (which must remain constant for two events)
V = V0 + V0 a ?T
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
I = -(c ?t)^2 + d^2
N²/Z (m_elec/m_red)

48. EM: Reactance of Capacitor
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Dv = -udm/m - v = v0 + u ln(m0/m)
PdV +dU
X_C = 1/(i?C)

49. Mech: Centripetal Force
S = k ln[O] ; dS = dQ/T
V = -L di/dt
F = mv²/r
U = t^2 d/dt (logZ)

50. Atom: Bohr Theory Ionization
E = Z²*E1
u dm/dt
Measurements close to true value
?s = 0 - ?l = ±1