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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. Single Slit Diffraction Maximum
<?|O|?>
Asin(?) = m?
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

2. Electromotive Force
C_eq = (? 1/C_i)^-1
I = I_cm + md²
DW/dq
Always Real

3. Quant: Eigenvalue of Hermitian Operator
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
B = µ0 I n
T = I?²/2
Always Real

4. Magnetic Field For Current in Long Wire
C = 4pe0 ab/(a-b) = inner and outer radii
µ0 I / 2pR
P/A = s T^4
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

5. Mech: Rotational Energy
S_mean = s/Sqrt[N]
F = -2*m(? x r)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
T = I?²/2

6. Self Inductance
<T> = 1/2 * <dV/dx>
DS = 0 - dQ = 0 - P V^? = constant
C = 4pe0 ab/(a-b) = inner and outer radii
V = -L di/dt

7. Rocket Thrust
I_z = I_x + I_y (think hoop symmetry)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Cv = dE/dT = 3R
u dm/dt

8. Astro: Kepler'S Third Law
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
DW/dq
Opposing charge induced upon conductor
P² ~ R³

9. Rayleigh criterion
F = R/2
qvb = mv²/R
? = 1.22? / d
Braking Radiation

10. Mech: Centripetal Force
?mc²
KE = 1/2 * µ (dr/dt)² L = µ r x v
F = mv²/r
V = -L di/dt

11. Quant: Orthogonality of States
I = -(c ?t)^2 + d^2
Infinitely close to equilibrium at all times
?= h/v(2mE)
<?1|?2> = 0 ? Orthogonal

12. Clausius-Clapeyron Equation
Dp/dt = L / (t ?V)
?~1/T
X_C = 1/(i?C)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

13. Perpendicular axis theorem
E = <?| H |?>
B = µ0 I n
I_z = I_x + I_y (think hoop symmetry)
.5 CV²

14. Pauli matrices
DS = 0 - dQ = 0 - P V^? = constant
Infinitely close to equilibrium at all times
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
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

15. EM: Electromagnetic inertia
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Faraday/Lenz: current inducted opposes the changing field
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
?~T

16. Magnetic Dipole Moment and Torque
µ = Current * Area T = µ x B
Int ( A . dr) = Int ( del x A) dSurface
U - ts = -tlog(Z)
E = s/e_0

17. Resistance - length - area - rho
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
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Dp/dt = L / (t ?V)

18. Thermo: 1st Law
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
H = H_0 + ?H
V = V0 + V0 a ?T
dQ = dW +dU

19. Thermo: Average Total Energy
Infinitely close to equilibrium at all times
X_C = 1/(i?C)
I = I_cm + md²
(° of Freedom)kT/2

20. De Broigle Wavelength
C_eq = ?C_i
?max = 2.898 x 10 -³ / T
Measurements close to true value
? = h/mv

21. Time Lorentz Transformation
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
µ0 I / 2R
? (t-vx/c²)

22. De Broglie wavelength
dU = 0 ? dS = ?dW/T
I = V/R exp(-t/RC)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
? = h/p

23. Thin Film Theory: Constructive / Destructive Interference
Const: 2t = (n +.5)? Destructive 2t = n?
C_eq = (? 1/C_i)^-1
Z²/n² (m_red/m_elec)
Dv = -udm/m - v = v0 + u ln(m0/m)

24. E field of a capacitor (d->0)
Sin(?) = ?/d
P +1/2 ? v² + ?gh = Constant
Z²/n² (m_red/m_elec)
E = s/e_0

25. Energy in a Capacitor
.5 CV²
µ0 I / 2R
?max = 2.898 x 10 -³ / T
? exp(-e/t)

26. EM: Method of Images
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
? (t-vx/c²)
KE = 1/2 * µ (dr/dt)² L = µ r x v

27. Dulong Petit Law
Cv = dE/dT = 3R
PdV +dU
I = I_cm + (1/2)m d^2
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

28. Relativistic Momentum
?mc²
DW = P dV
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
?mv

29. Bernoulli Equation
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
µ0 I1I2 / (2pd)
Exp(N(µ-e)/t)
P +1/2 ? v² + ?gh = Constant

30. Astro: Aperture Formula (Rayleigh Criterion)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
? = 1.22?/D
M? = 2dsin(?)
Sin(?) = ?/d

31. Energy in Inductor
F = mv²/r
PdV +dU
?? = h/mc * (1-cos(?))
.5 LI²

32. EM: Bremsstrahlung (translation)
Braking Radiation
?= h/v(2mE)
Exponentially decreasing radial function
Cv = dE/dT = 3R

33. Invariant Energy Quantity
Sin(?) = ?/d
I_z = I_x + I_y (think hoop symmetry)
E²-p²c²
F = I L X B

34. Single Slit Diffraction Intensity
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Measurements close to true value
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
u dm/dt

35. Kepler'S third law (T and R)
? = 1.22?/D
X_L = X_C or X_total = 0
? = 5/3
T^2 = k R^3 - k=constant

36. Stoke'S Theorem
Z_c = -i/(?C) ; Z_L = i ? L
Braking Radiation
Int ( A . dr) = Int ( del x A) dSurface
I_z = I_x + I_y (think hoop symmetry)

37. Wein'S Displacement Law
?s = 0 - ?l = ±1
F_f = µ*F_N
B = µ0 I n
?max = 2.898 x 10 -³ / T

38. Quant: Expectation Value
I = I_cm + (1/2)m d^2
NC?T
Z = ?g_i*exp(-E/kT)
<?|O|?>

39. Mech: Impulse
ds² = (c*dt)² - ?(x_i)²
Exponentially decreasing radial function
DS = 0 - dQ = 0 - P V^? = constant
J = ? Fdt

40. Parallel axis theorem
(3/2) n R ?t
I = I_cm + (1/2)m d^2
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

41. Atom: Orbital Config
DW = P dV
? = 1.22? / d
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
KE = 1/2 * µ (dr/dt)² L = µ r x v

42. Rocket Equation
Dv = -udm/m - v = v0 + u ln(m0/m)
F = µ0 q v I / 2pr
<T> = -<V>/2
<?1|?2> = 0 ? Orthogonal

43. Weighted average (mean and unc. of mean)
Sin(?) = ?/d
? = 1.22?/D
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
dQ = dW +dU

44. Helmholtz Free Energy
U - ts = -tlog(Z)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
qvb = mv²/R
Infinitely close to equilibrium at all times

45. EM: Reactance of Capacitor
C_eq = (? 1/C_i)^-1
?max = 2.898 x 10 -³ / T
?mc²
X_C = 1/(i?C)

46. Bar magnets -- direction of B field lines - earth'S B field
Isentropic
?= h/v(2mE)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
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.

47. 3 Laws of Thermo
?~T
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Hbar*?³/(p²c³exp(hbar?/t)-1)

48. QM: de Broglie Wavelength
?= h/v(2mE)
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.
P² ~ R³
NC?T

49. Work in a capacitor
X_L = i?L
V = -L di/dt
<T> = -<V>/2
1/2 CV²

50. Center of Mass: Kinetic Energy & Angular Momentum
KE = 1/2 * µ (dr/dt)² L = µ r x v
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.
dQ = dW +dU
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

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