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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. Angular momentum - Central Force Motion
L = mr²d?/dt
DW = P dV
<T> = -<V>/2
I = I_cm + (1/2)m d^2

2. Malus Law

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3. Perpendicular axis theorem
Infinitely close to equilibrium at all times
Ct²-x²-y²-z²
4H + 2e- ? He +2? + 6?
I_z = I_x + I_y (think hoop symmetry)

4. EM: Reactance of Capacitor
X_C = 1/(i?C)
DW/dq
? = ?0 root((1-v/c)/(1+v/c))
DW = P dV

5. EM: Bremsstrahlung (translation)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
E = <?| H |?>
Braking Radiation
?_max = b/T

6. Kepler'S third law (T and R)
T^2 = k R^3 - k=constant
? = 5/3
(3/2) n R ?t
?_max = b/T

7. Error in the mean if each measurement has the same uncertainty s
P/A = s T^4
v(mean)
µ0 I / 2pR
S_mean = s/Sqrt[N]

8. Adiabatic processes (dS - dQ - P and V)
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
U = t^2 d/dt (logZ)
W_A < W_I
DS = 0 - dQ = 0 - P V^? = constant

9. Magnetic Field of a long solenoid
B = µ0 I n
C_eq = (? 1/C_i)^-1
E = s/e_0
J = ? Fdt

10. Lab: Accuracy of Measurements
Ct²-x²-y²-z²
Measurements close to true value
I = V/R exp(-t/RC)
?= h/v(2mE)

11. Quant: [L_x -L_y] = ?
DW/dq
<T> = 1/2 * <dV/dx>
ih_barL_z
Exp(N(µ-e)/t)

12. EM: Series Capacitance
C_eq = (? 1/C_i)^-1
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Isentropic
Q = CVexp(-t/RC)

13. Law of Mass Action
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
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.
?~T
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

14. Planck Radiation Law
F = s * T4
Hbar*?³/(p²c³exp(hbar?/t)-1)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Always Real

15. Hall Coefficient
.5 LI²
ma + kx = 0
1/ne - where n is charge carrier density
Z = ?g_i*exp(-E/kT)

16. Source Free RL Circuit
Sin(?) = ?/d
dU = 0 ? dS = ?dW/T
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

17. Biot-Savart law
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
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
B = µ0 I n
E = s/e_0

18. Thermo: Isothermal
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
dU = 0 ? dS = ?dW/T
.5 CV²
Z²/n² (m_red/m_elec)

19. Triplet/singlet states: symmetry and net spin
?max = 2.898 x 10 -³ / T
.5 CV²
M? = 2dsin(?)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

20. RLC resonance condition
?? = h/mc * (1-cos(?))
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
? = 5/3
T^2 = k R^3 - k=constant

21. Gibbs Factor
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Exp(N(µ-e)/t)
X_L = X_C or X_total = 0

22. Quant: Eigenvalue of Hermitian Operator
Always Real
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Cv = dE/dT = 3R
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

23. Delta Function Potential - type of WF
P² ~ R³
?mc²
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Dv = -udm/m - v = v0 + u ln(m0/m)

24. Mech: Centripetal Force
N²/Z (m_elec/m_red)
F = mv²/r
N d flux / dt
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

25. Bohr Model: Energy
A[B -C] + [A -C]B
Z²/n² (m_red/m_elec)
Faraday/Lenz: current inducted opposes the changing field
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

26. Thermo: Blackbody Radiation
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
µ = Current * Area T = µ x B
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
F = s * T4

27. Wein'S Displacement Law
?max = 2.898 x 10 -³ / T
?_max = b/T
?~T
1/ne - where n is charge carrier density

28. Perturbations
v(mean)
U - ts = -tlog(Z)
H = H_0 + ?H
PdV +dU

29. Source-free RC Circuit
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
?mv
? = h/p
C_eq = (? 1/C_i)^-1

30. Parallel axis theorem
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Q = CVexp(-t/RC)
I = I_cm + (1/2)m d^2
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

31. EM: SHO (Hooke)
4H + 2e- ? He +2? + 6?
ma + kx = 0
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
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.

32. Solid: Resistivity of Metal
I = -(c ?t)^2 + d^2
L = T - V dL/dq = d/dt dL/dqdot
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
?~T

33. EM: AC Resonance
E²-p²c²
U = t^2 d/dt (logZ)
DS = 0 - dQ = 0 - P V^? = constant
X_L = X_C or X_total = 0

34. Single Slit Diffraction Maximum
Q = CVexp(-t/RC)
dU = 0 ? dS = ?dW/T
Asin(?) = m?
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

35. Hamiltonian and Hamilton'S equations
F = f* (c+v_r)/(c+v_s)
1/ne - where n is charge carrier density
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

36. Internal Energy of an Ideal Gas
Z_c = -i/(?C) ; Z_L = i ? L
Measurements close to mean
<T> = -<V>/2
(3/2) n R ?t

37. Energy in Inductor
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Hbar*?³/(p²c³exp(hbar?/t)-1)
L = T - V dL/dq = d/dt dL/dqdot
.5 LI²

38. De Broigle Wavelength
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
F = mv²/r
? = h/mv

39. Doppler Shift in Frequency
F = f* (c+v_r)/(c+v_s)
F = s * T4
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
DS = 0 - dQ = 0 - P V^? = constant

40. Relativistic Momentum
?mv
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
? = h/p
P² ~ R³

41. Radiation (Larmor - and another neat fact)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
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
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
F = I L X B

42. Mech: Rotational Energy
T = I?²/2
<?|O|?>
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.
Dp/dt = L / (t ?V)

43. EM: Method of Images
Opposing charge induced upon conductor
F = R/2
u dm/dt
<?1|?2> = 0 ? Orthogonal

44. Thermo: 1st Law
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
dQ = dW +dU
<?1|?2> = 0 ? Orthogonal
?~T

45. Force on a wire in magnetic field
U = t^2 d/dt (logZ)
F = I L X B
µ0 I / 2R
µ0 I1I2 / (2pd)

46. Stefan-Boltzmann law for blackbodies (power per area and T)
v(mean)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
dQ = dW +dU
P/A = s T^4

47. Rocket Thrust
?mv
u dm/dt
Cv = dE/dT = 3R
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

48. Thermo: Partition Function
J = ? Fdt
Z = ?g_i*exp(-E/kT)
?mv
dQ = dW +dU

49. Quant: Expectation Value
? = h/mv
N d flux / dt
<?|O|?>
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

50. Atom: Bohr Theory Ionization
? = 1.22?/D
T^2 = k R^3 - k=constant
E = Z²*E1
M? = 2dsin(?)