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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. EM: Reactance of Inductor
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
X_L = i?L
I = V/R exp(-t/RC)
T^2 = k R^3 - k=constant

2. Resistance - length - area - rho
I = I_0 Cos[?]^2
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
ma + kx = 0
.5 LI²

3. Kepler'S third law (T and R)
dQ = dW +dU
B = µ0 I n
T^2 = k R^3 - k=constant
L = L_0 Sqrt[1-v^2/c^2]

4. EM: Reactance of Capacitor
PdV +dU
X_C = 1/(i?C)
Infinitely close to equilibrium at all times
v(mean)

5. EM: Parallel Capacitance
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
<?|O|?>
N d flux / dt
C_eq = ?C_i

6. Time Lorentz Transformation
PdV +dU
? (t-vx/c²)
S = k ln[O] ; dS = dQ/T
ih_barL_z

7. Thermo: Adiabatic Work vs Isothermal Work
Sin(?) = ?/d
µ0 I1I2 / (2pd)
F = -2*m(? x r)
W_A < W_I

8. Relativistic Energy
?mc²
? exp(-e/t)
?? = h/mc * (1-cos(?))
P1V1 - P2V2 / (? - 1)

9. Virial Theorem
I = I_cm + (1/2)m d^2
<T> = 1/2 * <dV/dx>
A[B -C] + [A -C]B
? = ?0 root((1-v/c)/(1+v/c))

10. Current in resistor in RC circuit
P² ~ R³
DW/dq
I = V/R exp(-t/RC)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

11. Addition of relativistic velocities

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12. Solid: Resistivity of Metal
u dm/dt
?~T
E²-p²c²
µ0 I / 2R

13. Thermo: Partition Function
F = qv×B
B = µ0 I n
Z = ?g_i*exp(-E/kT)
DW = P dV

14. td(entropy) =
P/A = s T^4
PdV +dU
.5 LI²
dQ = dW +dU

15. Relativistic Momentum
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
?mv
? = h/mv
M? = 2dsin(?)

16. Pauli matrices
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
Braking Radiation
S_mean = s/Sqrt[N]
L = T - V dL/dq = d/dt dL/dqdot

17. Mech: Rotational Energy
I = -(c ?t)^2 + d^2
T = I?²/2
V(r) + L²2/2mr²
F = qv×B

18. EM: Maxwell'S equations
E = <?| H |?>
ma + kx = 0
(3/2) n R ?t
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

19. De Broigle Wavelength
.5 LI²
0
? = 5/3
? = h/mv

20. QM: de Broglie Wavelength
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Measurements close to true value
(3/2) n R ?t
?= h/v(2mE)

21. Lensmaker Equation - Thin Lens
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
F = f* (c+v_r)/(c+v_s)
V = V0 + V0 a ?T

22. Angular momentum - Central Force Motion
X_L = X_C or X_total = 0
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
P/A = s T^4
L = mr²d?/dt

23. Atom: Hydrogen Wave Function Type
Exponentially decreasing radial function
F = f* (c+v_r)/(c+v_s)
I = I_cm + md²
? = 5/3

24. Work done on a gas
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
DW = P dV
ih_barL_z
S_mean = s/Sqrt[N]

25. Double Slit: Interference Minimum - Diffraction Minimum
1/ne - where n is charge carrier density
Hbar*?³/(p²c³exp(hbar?/t)-1)
u dm/dt
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

26. Thermo: Blackbody Radiation
1/vLC
F = s * T4
Exponentially decreasing radial function
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

27. Relativistic interval (which must remain constant for two events)
X_C = 1/(i?C)
? = h/mv
I = -(c ?t)^2 + d^2
S_mean = s/Sqrt[N]

28. SR: Total Energy of a Particle
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
µ=s^2
Int ( A . dr) = Int ( del x A) dSurface

29. EM: Method of Images
(° of Freedom)kT/2
Opposing charge induced upon conductor
? = h/p
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

30. Atom: Positronium Reduced Mass
Dp/dt = L / (t ?V)
Faraday/Lenz: current inducted opposes the changing field
? (t-vx/c²)
µ = m_e/2

31. Lab: Precision of Measurements
Measurements close to mean
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
P +1/2 ? v² + ?gh = Constant
F = I L X B

32. Source-free RC Circuit
I = I_0 Cos[?]^2
µ0 I1I2 / (2pd)
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
B = µ0 I n

33. EM: Bremsstrahlung (translation)
F = R/2
F = I L X B
4H + 2e- ? He +2? + 6?
Braking Radiation

34. Helmholtz Free Energy
I = -(c ?t)^2 + d^2
?s = 0 - ?l = ±1
µ = m_e/2
U - ts = -tlog(Z)

35. How to derive cylcotron frequency
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
qvb = mv²/R
P +1/2 ? v² + ?gh = Constant
I = I_cm + md²

36. Invariant spatial quantity
Ct²-x²-y²-z²
F = f* (c+v_r)/(c+v_s)
?mv
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

37. Thermo: Isothermal
µ = Current * Area T = µ x B
Z²/n² (m_red/m_elec)
?~1/T
dU = 0 ? dS = ?dW/T

38. Hall Coefficient
Dv = -udm/m - v = v0 + u ln(m0/m)
P² ~ R³
1/ne - where n is charge carrier density
V(r) + L²2/2mr²

39. Thermo: Average Total Energy
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
(° of Freedom)kT/2
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

40. Entropy (# of states - and in terms of other thermo quantities)
S = k ln[O] ; dS = dQ/T
? = 1.22?/D
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
µ = Current * Area T = µ x B

41. EM: Lorentz Force
? = h/p
Exponentially decreasing radial function
? = 1.22?/D
F = qv×B

42. Mech: Parallel Axis Theorem (Moment of Inertia)
I = I_cm + md²
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
P/A = s T^4
F = f* (c+v_r)/(c+v_s)

43. Center of Mass: Kinetic Energy & Angular Momentum
F_f = µ*F_N
v(mean)
KE = 1/2 * µ (dr/dt)² L = µ r x v
F = qv×B

44. Planck Radiation Law
Asin(?) = m?
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
P +1/2 ? v² + ?gh = Constant
Hbar*?³/(p²c³exp(hbar?/t)-1)

45. Force exerted on charge by long wire
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.
µ = Current * Area T = µ x B
F = µ0 q v I / 2pr
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

46. Heat added
F = mv²/r
PdV +dU
NC?T
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

47. Error in the mean if each measurement has the same uncertainty s
?? = h/mc * (1-cos(?))
Ct²-x²-y²-z²
S_mean = s/Sqrt[N]
F = qv×B

48. Spherical Capacitor Equation
NC?T
P/A = s T^4
? = ?0 root((1-v/c)/(1+v/c))
C = 4pe0 ab/(a-b) = inner and outer radii

49. SR: Spacetime Interval
u dm/dt
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
C_eq = ?C_i
ds² = (c*dt)² - ?(x_i)²

50. Rayleigh'S Criterion
Sin(?) = ?/d
F = µ0 q v I / 2pr
? = 1.22?/D
ma + kx = 0

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