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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. Lensmaker Equation - Thin Lens
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
4H + 2e- ? He +2? + 6?
Infinitely close to equilibrium at all times
S_mean = s/Sqrt[N]

2. Relativistic length contraction
U - ts = -tlog(Z)
µ=s^2
L = L_0 Sqrt[1-v^2/c^2]
Infinitely close to equilibrium at all times

3. Poisson distribution (µ and s)
?? = h/mc * (1-cos(?))
µ=s^2
E = Z²*E1
? = h/p

4. EM: Parallel Capacitance
V(r) + L²2/2mr²
I = V/R exp(-t/RC)
P1V1 - P2V2 / (? - 1)
C_eq = ?C_i

5. EM: Bremsstrahlung (translation)
U = t^2 d/dt (logZ)
µ0 I / 2pR
µ0 I1I2 / (2pd)
Braking Radiation

6. Angular momentum operators L^2 and L_z
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Q = CVexp(-t/RC)
.5 CV²

7. Magnetic Dipole Moment and Torque
µ0 I / 2pR
Asin(?) = m?
T = I?²/2
µ = Current * Area T = µ x B

8. Thermo: Monatomic gas ?=?
Asin(?) = m?
µ0 I / 2R
? = 5/3
? = ?0 root((1-v/c)/(1+v/c))

9. Compton Scattering
I = -(c ?t)^2 + d^2
Exponentially decreasing radial function
Braking Radiation
?? = h/mc * (1-cos(?))

10. Inductance of Solenoid
?max = 2.898 x 10 -³ / T
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
<?1|?2> = 0 ? Orthogonal
Sin(?) = ?/d

11. Coriolis Force
4H + 2e- ? He +2? + 6?
F = -2*m(? x r)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
I = V/R exp(-t/RC)

12. Helmholtz Free Energy
? = 5/3
P/A = s T^4
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
U - ts = -tlog(Z)

13. Thermo: Partition Function
Exp(N(µ-e)/t)
Infinitely close to equilibrium at all times
I = I_0 Cos[?]^2
Z = ?g_i*exp(-E/kT)

14. EM: AC Resonance
X_L = X_C or X_total = 0
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Dv = -udm/m - v = v0 + u ln(m0/m)
Cos[?] Sin[?] -Sin[?] Cos[?]

15. Magnetic Field Through Ring
ds² = (c*dt)² - ?(x_i)²
µ0 I / 2R
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
N²/Z (m_elec/m_red)

16. EM: SHO (Hooke)
I = I_cm + md²
ma + kx = 0
C_eq = (? 1/C_i)^-1
Q = CVexp(-t/RC)

17. Wein'S displacement law for blackbodies (? and T)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
µ0 I / 2pR
Hbar*?³/(p²c³exp(hbar?/t)-1)
?_max = b/T

18. Quant: Expectation Value
L = L_0 Sqrt[1-v^2/c^2]
Exponentially decreasing radial function
<?|O|?>
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

19. Solid: Resistivity of Semi-Conductor
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
µ = Current * Area T = µ x B
?~1/T
Hbar*?³/(p²c³exp(hbar?/t)-1)

20. EM: Maxwell'S equations
ma + kx = 0
I = -(c ?t)^2 + d^2
I ' = I cos²(?)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

21. Single Slit Diffraction Intensity
P/A = s T^4
?s = 0 - ?l = ±1
Measurements close to true value
I = Im (sinc²(a)) ; a = pai sin(?) / ?

22. Springs in series/parallel
Ct²-x²-y²-z²
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
E²-p²c²

23. Triplet/singlet states: symmetry and net spin
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Dp/dt = L / (t ?V)
H = H_0 + ?H
? exp(-e/t)

24. Mech: Centripetal Force
DW = P dV
Faraday/Lenz: current inducted opposes the changing field
? = 5/3
F = mv²/r

25. Electromotive Force
I = Im (sinc²(a)) ; a = pai sin(?) / ?
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
W_A < W_I
DW/dq

26. Focal point of mirrror with curvature
M? = 2dsin(?)
? (t-vx/c²)
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.
F = R/2

27. Quant: [L_x -L_y] = ?
J = E s - s = Conductivity - E = Electric field
ih_barL_z
PdV +dU
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

28. Relativistic Energy
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
?mc²
W_A < W_I
Measurements close to true value

29. Dulong Petit Law
Z = ?g_i*exp(-E/kT)
Cv = dE/dT = 3R
M? = 2dsin(?)
P² ~ R³

30. Quant: Commutator Relation [AB -C]
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.
J = E s - s = Conductivity - E = Electric field
A[B -C] + [A -C]B
L = mr²d?/dt

31. Kepler'S third law (T and R)
µ=s^2
T^2 = k R^3 - k=constant
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Always Real

32. SR: Spacetime Interval
v(mean)
T = I?²/2
ds² = (c*dt)² - ?(x_i)²
ih_barL_z

33. Adiabatic means
?mc²
Hbar*?³/(p²c³exp(hbar?/t)-1)
Isentropic
?= h/v(2mE)

34. SR: Total Energy of a Particle
?= h/v(2mE)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
H = H_0 + ?H
F = -2*m(? x r)

35. 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.
S = k ln[O] ; dS = dQ/T
F = qv×B
F = I L X B

36. Anomalous Zeeman Effect

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37. Invariant Energy Quantity
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
V = -L di/dt
E²-p²c²
Ct²-x²-y²-z²

38. Force on a wire in magnetic field
Cos[?] Sin[?] -Sin[?] Cos[?]
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
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
F = I L X B

39. Thermo: Isothermal
<T> = -<V>/2
1/2 CV²
dU = 0 ? dS = ?dW/T
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

40. Error in the mean if each measurement has the same uncertainty s
S_mean = s/Sqrt[N]
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
PdV +dU

41. QM: de Broglie Wavelength
Dv = -udm/m - v = v0 + u ln(m0/m)
Int ( A . dr) = Int ( del x A) dSurface
?= h/v(2mE)
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. Time Lorentz Transformation
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
? (t-vx/c²)
? exp(-e/t)
?= h/v(2mE)

43. Atom: Bohr Formula
<?|O|?>
<T> = -<V>/2
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
?~1/T

44. Solid: Resistivity of Metal
?~T
? = ?0 root((1-v/c)/(1+v/c))
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

45. Lab: Accuracy of Measurements
? = 1.22? / d
Always Real
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Measurements close to true value

46. Malus Law

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47. Rocket Equation
ih_barL_z
Dv = -udm/m - v = v0 + u ln(m0/m)
C = 4pe0 ab/(a-b) = inner and outer radii
? exp(-e/t)

48. Entropy (# of states - and in terms of other thermo quantities)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
V = -L di/dt
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
S = k ln[O] ; dS = dQ/T

49. Thermo: Blackbody Radiation
F = s * T4
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
U = t^2 d/dt (logZ)
C = 4pe0 ab/(a-b) = inner and outer radii

50. Mech: Virial Theorem
S_mean = s/Sqrt[N]
F = f* (c+v_r)/(c+v_s)
<T> = -<V>/2
Cv = dE/dT = 3R