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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. Induced EMF of solenoid
N²/Z (m_elec/m_red)
?~1/T
N d flux / dt
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

2. First law of thermodynamics (explain direction of energy for each term)
KE = 1/2 * µ (dr/dt)² L = µ r x v
E = s/e_0
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
B = µ0 I n

3. Atom: Bohr Theory Ionization
F = R/2
V(r) + L²2/2mr²
E = Z²*E1
v(mean)

4. Resonance frequency of LC circuit
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
1/vLC
Measurements close to mean
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

5. Radiation (Larmor - and another neat fact)
?= h/v(2mE)
Cos[?] Sin[?] -Sin[?] Cos[?]
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
µ=s^2

6. Addition of relativistic velocities

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7. Astro: Aperture Formula (Rayleigh Criterion)
µ = m_e/2
? = 1.22?/D
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

8. Inductance of Solenoid
ma + kx = 0
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Always Real
0

9. EM: Electric Field inside of Conductor
µ=s^2
? = h/mv
0
µ0 I / 2pR

10. Kepler'S Three Laws
P² ~ R³
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
1/2 CV²
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

11. Rayleigh criterion
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
NC?T
?max = 2.898 x 10 -³ / T
? = 1.22? / d

12. Springs in series/parallel
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
P +1/2 ? v² + ?gh = Constant
Infinitely close to equilibrium at all times
S_mean = s/Sqrt[N]

13. Adiabatic means
Isentropic
.5 CV²
?mc²
F = R/2

14. Hall Coefficient
S_mean = s/Sqrt[N]
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
1/ne - where n is charge carrier density
Opposing charge induced upon conductor

15. Poisson distribution (µ and s)
H = H_0 + ?H
(° of Freedom)kT/2
I = I_0 Cos[?]^2
µ=s^2

16. Self Inductance
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
F = µ0 q v I / 2pr
Measurements close to mean
V = -L di/dt

17. EM: Electromagnetic inertia
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Faraday/Lenz: current inducted opposes the changing field
A[B -C] + [A -C]B
I = -(c ?t)^2 + d^2

18. Mech: Rotational Energy
T = I?²/2
Measurements close to true value
Exp(N(µ-e)/t)
I_z = I_x + I_y (think hoop symmetry)

19. Lab: Standard Deviation of Poisson
Infinitely close to equilibrium at all times
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
v(mean)

20. Relativistic Energy
N²/Z (m_elec/m_red)
?_max = b/T
?~T
?mc²

21. Astro: Kepler'S Third Law
Infinitely close to equilibrium at all times
V(r) + L²2/2mr²
P² ~ R³
? = ?0 root((1-v/c)/(1+v/c))

22. Relativistic Momentum
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
W_A < W_I
?mv

23. Stark Effect
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
Measurements close to true value
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
T^2 = k R^3 - k=constant

24. EM: Lorentz Force
Cos[?] Sin[?] -Sin[?] Cos[?]
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
F = qv×B
?~T

25. Perpendicular axis theorem
ma + kx = 0
I = V/R exp(-t/RC)
I_z = I_x + I_y (think hoop symmetry)
C_eq = (? 1/C_i)^-1

26. De Broigle Wavelength
? = h/p
0
<T> = 1/2 * <dV/dx>
? = h/mv

27. Thermo: Average Total Energy
(° of Freedom)kT/2
? (t-vx/c²)
4H + 2e- ? He +2? + 6?
Always Real

28. Atom: Bohr Formula
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
F = µ0 q v I / 2pr
L = L_0 Sqrt[1-v^2/c^2]
E²-p²c²

29. Quant: Orthogonality of States
<?1|?2> = 0 ? Orthogonal
N²/Z (m_elec/m_red)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
ds² = (c*dt)² - ?(x_i)²

30. EM: SHO (Hooke)
1/2 CV²
F = qv×B
ma + kx = 0
U = t^2 d/dt (logZ)

31. Quant: Expectation Value
<?|O|?>
E²-p²c²
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
1/vLC

32. Wein'S Displacement Law
?max = 2.898 x 10 -³ / T
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.
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

33. Complex impedance (expressions for capacitor and inductor)
Z_c = -i/(?C) ; Z_L = i ? L
?s = 0 - ?l = ±1
? = 5/3
N d flux / dt

34. Solid: Resistivity of Metal
I = I_0 Cos[?]^2
?~T
I = Im (sinc²(a)) ; a = pai sin(?) / ?
C_eq = ?C_i

35. Thin Film Theory: Constructive / Destructive Interference
Hbar*?³/(p²c³exp(hbar?/t)-1)
? = h/p
µ0 I / 2R
Const: 2t = (n +.5)? Destructive 2t = n?

36. Mech: Virial Theorem
E²-p²c²
C_eq = (? 1/C_i)^-1
<T> = -<V>/2
Q = CVexp(-t/RC)

37. Lab: Accuracy of Measurements
Measurements close to true value
?mc²
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

38. Volumetric Expansion
V = V0 + V0 a ?T
B = µ0 I n
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
Braking Radiation

39. Kepler'S third law (T and R)
Z²/n² (m_red/m_elec)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
T^2 = k R^3 - k=constant
I = I_cm + md²

40. Angular momentum operators L^2 and L_z
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
F = -2*m(? x r)
?= h/v(2mE)
Const: 2t = (n +.5)? Destructive 2t = n?

41. Invariant spatial quantity
.5 CV²
Ct²-x²-y²-z²
E = <?| H |?>
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

42. Error in the mean if each measurement has the same uncertainty s
S_mean = s/Sqrt[N]
X_C = 1/(i?C)
X_L = i?L
P +1/2 ? v² + ?gh = Constant

43. QM: de Broglie Wavelength
M? = 2dsin(?)
X_C = 1/(i?C)
.5 CV²
?= h/v(2mE)

44. Energy in Inductor
NC?T
.5 LI²
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
? = 5/3

45. Triplet/singlet states: symmetry and net spin
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
T^2 = k R^3 - k=constant
F = s * T4
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

46. Clausius-Clapeyron Equation
Infinitely close to equilibrium at all times
Dv = -udm/m - v = v0 + u ln(m0/m)
N d flux / dt
Dp/dt = L / (t ?V)

47. Energy in terms of partition function
U = t^2 d/dt (logZ)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
F = µ0 q v I / 2pr
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

48. Rotation matrix (2x2)
I = V/R exp(-t/RC)
Cos[?] Sin[?] -Sin[?] Cos[?]
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
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.

49. Mech: Impulse
J = ? Fdt
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
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.
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

50. EM: Reactance of Capacitor
I = I_0 Cos[?]^2
X_C = 1/(i?C)
µ = m_e/2
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas