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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. Magnetic Field For Current in Long Wire
V(r) + L²2/2mr²
µ0 I / 2pR
U - ts = -tlog(Z)
? = h/p

2. RLC resonance condition
Z²/n² (m_red/m_elec)
Infinitely close to equilibrium at all times
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

3. Force/length between two wires
Sin(?) = ?/d
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
µ0 I1I2 / (2pd)
ds² = (c*dt)² - ?(x_i)²

4. EM: Electric Field inside of Conductor
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
4H + 2e- ? He +2? + 6?
0
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

5. Single Slit Diffraction Maximum
S = k ln[O] ; dS = dQ/T
Asin(?) = m?
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.
Opposing charge induced upon conductor

6. Charge in Capacitor
F = R/2
<T> = -<V>/2
Q = CVexp(-t/RC)
DW = P dV

7. Rayleigh'S Criterion
Sin(?) = ?/d
I ' = I cos²(?)
P/A = s T^4
S = k ln[O] ; dS = dQ/T

8. Thermo: Isothermal
P² ~ R³
Ct²-x²-y²-z²
dU = 0 ? dS = ?dW/T
Opposing charge induced upon conductor

9. Adiabatic processes (dS - dQ - P and V)
W_A < W_I
V = V0 + V0 a ?T
ih_barL_z
DS = 0 - dQ = 0 - P V^? = constant

10. Stefan-Boltzmann law for blackbodies (power per area and T)
? = ?0 root((1-v/c)/(1+v/c))
F = -2*m(? x r)
<?1|?2> = 0 ? Orthogonal
P/A = s T^4

11. Work in a capacitor
1/2 CV²
A[B -C] + [A -C]B
I = Im (sinc²(a)) ; a = pai sin(?) / ?
1/ne - where n is charge carrier density

12. Heat added
T^2 = k R^3 - k=constant
J/(ne) n: atom density
NC?T
? (t-vx/c²)

13. Compton Scattering
Isentropic
PdV +dU
?? = h/mc * (1-cos(?))
(3/2) n R ?t

14. Kepler'S Three Laws
W_A < W_I
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Cos[?] Sin[?] -Sin[?] Cos[?]
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

15. EM: Reactance of Capacitor
µ = m_e/2
? exp(-e/t)
X_C = 1/(i?C)
4H + 2e- ? He +2? + 6?

16. Gibbs Factor
I_z = I_x + I_y (think hoop symmetry)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
F = I L X B
Exp(N(µ-e)/t)

17. Mean electron drift speed
J/(ne) n: atom density
V = V0 + V0 a ?T
1/vLC
Sin(?) = ?/d

18. Magnetic Field Through Ring
T^2 = k R^3 - k=constant
Opposing charge induced upon conductor
µ0 I / 2R
4H + 2e- ? He +2? + 6?

19. Double Slit: Interference Minimum - Diffraction Minimum
X_L = X_C or X_total = 0
qvb = mv²/R
H = H_0 + ?H
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

20. Astro: p-p Chain
4H + 2e- ? He +2? + 6?
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
ih_barL_z
I = I_cm + (1/2)m d^2

21. Quant: Expectation Value
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Measurements close to mean
<?|O|?>
Faraday/Lenz: current inducted opposes the changing field

22. SR: Spacetime Interval
ds² = (c*dt)² - ?(x_i)²
?s = 0 - ?l = ±1
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
F = s * T4

23. Invariant spatial quantity
ds² = (c*dt)² - ?(x_i)²
µ0 I / 2pR
Ct²-x²-y²-z²
Z²/n² (m_red/m_elec)

24. Rotation matrix (2x2)
µ0 I1I2 / (2pd)
Always Real
4H + 2e- ? He +2? + 6?
Cos[?] Sin[?] -Sin[?] Cos[?]

25. Doppler Shift in Frequency
DW/dq
µ0 I / 2pR
µ0 I / 2R
F = f* (c+v_r)/(c+v_s)

26. Hamiltonian and Hamilton'S equations
U - ts = -tlog(Z)
U = t^2 d/dt (logZ)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

27. Energy in terms of partition function
µ0 I / 2R
F = -2*m(? x r)
U = t^2 d/dt (logZ)
.5 CV²

28. 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.
qvb = mv²/R
B = µ0 I n
Sin(?) = ?/d

29. De Broigle Wavelength
E²-p²c²
? = h/mv
(° of Freedom)kT/2
V(r) + L²2/2mr²

30. Addition of relativistic velocities

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31. Doppler Shift for light
Exponentially decreasing radial function
? = ?0 root((1-v/c)/(1+v/c))
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
L = mr²d?/dt

32. SR: Total Energy of a Particle
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
qvb = mv²/R
ih_barL_z
F = f* (c+v_r)/(c+v_s)

33. 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
dU = 0 ? dS = ?dW/T
?~1/T
X_L = i?L

34. First law of thermodynamics (explain direction of energy for each term)
0
Always Real
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
?? = h/mc * (1-cos(?))

35. How to derive cylcotron frequency
qvb = mv²/R
J/(ne) n: atom density
?s = 0 - ?l = ±1
F = qv×B

36. Volumetric Expansion
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
? = 1.22?/D
V = V0 + V0 a ?T
L = T - V dL/dq = d/dt dL/dqdot

37. Thermo: Blackbody Radiation
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
µ0 I / 2pR
F = s * T4
C = 4pe0 ab/(a-b) = inner and outer radii

38. Internal Energy of an Ideal Gas
qvb = mv²/R
C_eq = ?C_i
(3/2) n R ?t
?max = 2.898 x 10 -³ / T

39. Rocket Thrust
u dm/dt
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
I = V/R exp(-t/RC)
Isentropic

40. Bernoulli Equation
P +1/2 ? v² + ?gh = Constant
qvb = mv²/R
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Opposing charge induced upon conductor

41. Energy in a Capacitor
µ = Current * Area T = µ x B
.5 CV²
T = I?²/2
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

42. Astro: Aperture Formula (Rayleigh Criterion)
? = 1.22?/D
ih_barL_z
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
µ = m_e/2

43. EM: Parallel Capacitance
C_eq = ?C_i
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Z = ?g_i*exp(-E/kT)
ih_barL_z

44. Force exerted on charge by long wire
F = µ0 q v I / 2pr
N²/Z (m_elec/m_red)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
P² ~ R³

45. Kepler'S third law (T and R)
T^2 = k R^3 - k=constant
V = V0 + V0 a ?T
µ0 I1I2 / (2pd)
C_eq = ?C_i

46. Time Lorentz Transformation
?max = 2.898 x 10 -³ / T
Int ( A . dr) = Int ( del x A) dSurface
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
? (t-vx/c²)

47. Virial Theorem
.5 LI²
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
<T> = 1/2 * <dV/dx>

48. Atom: Hydrogen Wave Function Type
Exponentially decreasing radial function
T = I?²/2
? = h/mv
L = L_0 Sqrt[1-v^2/c^2]

49. Helmholtz Free Energy
qvb = mv²/R
µ = m_e/2
U - ts = -tlog(Z)
.5 LI²

50. Induced EMF of solenoid
1/ne - where n is charge carrier density
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
N d flux / dt
Dv = -udm/m - v = v0 + u ln(m0/m)