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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. Relativistic Energy
I_z = I_x + I_y (think hoop symmetry)
?mc²
C_eq = (? 1/C_i)^-1
Exponentially decreasing radial function

2. RLC resonance condition
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Measurements close to mean
F_f = µ*F_N
Exp(N(µ-e)/t)

3. Mean electron drift speed
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
J/(ne) n: atom density
dQ = dW +dU
J = ? Fdt

4. EM: Maxwell'S equations
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
I = I_cm + (1/2)m d^2
J/(ne) n: atom density
?~T

5. Atom: Positronium Reduced Mass
M? = 2dsin(?)
µ = m_e/2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
N d flux / dt

6. Hamiltonian and Hamilton'S equations
I = Im (sinc²(a)) ; a = pai sin(?) / ?
W_A < W_I
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Int ( A . dr) = Int ( del x A) dSurface

7. Magnetic Dipole Moment and Torque
F = f* (c+v_r)/(c+v_s)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
I ' = I cos²(?)
µ = Current * Area T = µ x B

8. Bohr Model: Radii
N²/Z (m_elec/m_red)
1/2 CV²
H = H_0 + ?H
Exponentially decreasing radial function

9. Solid: Resistivity of Metal
F = µ0 q v I / 2pr
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
?~T
? = 5/3

10. Selection Rules
µ=s^2
F = R/2
?s = 0 - ?l = ±1
H = H_0 + ?H

11. Law of Mass Action
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
u dm/dt
Cos[?] Sin[?] -Sin[?] Cos[?]
Const: 2t = (n +.5)? Destructive 2t = n?

12. Angular momentum - Central Force Motion
L = mr²d?/dt
I = V/R exp(-t/RC)
Exp(N(µ-e)/t)
T = I?²/2

13. Relativistic interval (which must remain constant for two events)
I = -(c ?t)^2 + d^2
F = f* (c+v_r)/(c+v_s)
?= h/v(2mE)
ds² = (c*dt)² - ?(x_i)²

14. Energy in a Capacitor
E = s/e_0
X_L = i?L
L = L_0 Sqrt[1-v^2/c^2]
.5 CV²

15. Kepler'S third law (T and R)
T^2 = k R^3 - k=constant
.5 LI²
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
1/2 CV²

16. Center of Mass: Kinetic Energy & Angular Momentum
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
M? = 2dsin(?)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
KE = 1/2 * µ (dr/dt)² L = µ r x v

17. Mech: Force of Friction
Dv = -udm/m - v = v0 + u ln(m0/m)
F_f = µ*F_N
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.
X_L = X_C or X_total = 0

18. Lensmaker Equation - Thin Lens
L = L_0 Sqrt[1-v^2/c^2]
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
?mc²

19. Rotation matrix (2x2)
Isentropic
Cos[?] Sin[?] -Sin[?] Cos[?]
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
L = T - V dL/dq = d/dt dL/dqdot

20. Atom: Bohr Formula
F = I L X B
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
µ = Current * Area T = µ x B
Cv = dE/dT = 3R

21. Malus Law

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22. Pauli matrices
X_C = 1/(i?C)
Measurements close to true value
F = qv×B
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

23. EM: Reactance of Capacitor
X_C = 1/(i?C)
F = I L X B
U = t^2 d/dt (logZ)
F = µ0 q v I / 2pr

24. Thermo: 1st Law
C_eq = (? 1/C_i)^-1
? = 5/3
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
dQ = dW +dU

25. Error in the mean if each measurement has the same uncertainty s
P1V1 - P2V2 / (? - 1)
A[B -C] + [A -C]B
Asin(?) = m?
S_mean = s/Sqrt[N]

26. Parallel axis theorem
<?1|?2> = 0 ? Orthogonal
? = h/p
I = I_cm + (1/2)m d^2
Exp(N(µ-e)/t)

27. Mech: Centripetal Force
C = 4pe0 ab/(a-b) = inner and outer radii
F = mv²/r
Cv = dE/dT = 3R
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

28. Double Slit: Interference Minimum - Diffraction Minimum
? = 5/3
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
M? = 2dsin(?)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

29. Charge in Capacitor
Q = CVexp(-t/RC)
M? = 2dsin(?)
C_eq = ?C_i
Exponentially decreasing radial function

30. De Broigle Wavelength
µ0 I1I2 / (2pd)
? = h/mv
E = s/e_0
X_L = X_C or X_total = 0

31. Invariant Energy Quantity
E²-p²c²
S_mean = s/Sqrt[N]
J = ? Fdt
Dp/dt = L / (t ?V)

32. Relativistic Momentum
F = s * T4
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
?mv

33. Quant: Eigenvalue of Hermitian Operator
Always Real
1/2 CV²
I = -(c ?t)^2 + d^2
µ = m_e/2

34. EM: SHO (Hooke)
I = I_0 Cos[?]^2
I = I_cm + md²
ma + kx = 0
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

35. EM: Bremsstrahlung (translation)
? = h/mv
Braking Radiation
F = µ0 q v I / 2pr
ih_barL_z

36. Magnetic Field of a long solenoid
u dm/dt
C_eq = (? 1/C_i)^-1
B = µ0 I n
C = 4pe0 ab/(a-b) = inner and outer radii

37. Mech: Parallel Axis Theorem (Moment of Inertia)
KE = 1/2 * µ (dr/dt)² L = µ r x v
4H + 2e- ? He +2? + 6?
I = I_cm + md²
J = ? Fdt

38. Coriolis Force
F = -2*m(? x r)
.5 LI²
(° of Freedom)kT/2
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

39. Volumetric Expansion
V = V0 + V0 a ?T
F = f* (c+v_r)/(c+v_s)
F = -2*m(? x r)
DS = 0 - dQ = 0 - P V^? = constant

40. Delta Function Potential - type of WF
Exp(N(µ-e)/t)
J = ? Fdt
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Z = ?g_i*exp(-E/kT)

41. Thermo: Average Total Energy
(° of Freedom)kT/2
A[B -C] + [A -C]B
S_mean = s/Sqrt[N]
P² ~ R³

42. Clausius-Clapeyron Equation
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.
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Dp/dt = L / (t ?V)
J = E s - s = Conductivity - E = Electric field

43. Compton Scattering
X_L = i?L
Dv = -udm/m - v = v0 + u ln(m0/m)
?? = h/mc * (1-cos(?))
Cos[?] Sin[?] -Sin[?] Cos[?]

44. Adiabatic processes (dS - dQ - P and V)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
DS = 0 - dQ = 0 - P V^? = constant
Faraday/Lenz: current inducted opposes the changing field
v(mean)

45. EM: Electric Field inside of Conductor
C = 4pe0 ab/(a-b) = inner and outer radii
µ = m_e/2
0
PdV +dU

46. Boltzmann / Canonical distribution
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
V(r) + L²2/2mr²
X_L = X_C or X_total = 0
Infinitely close to equilibrium at all times

47. Poisson distribution (µ and s)
µ=s^2
L = T - V dL/dq = d/dt dL/dqdot
? = ?0 root((1-v/c)/(1+v/c))
I_z = I_x + I_y (think hoop symmetry)

48. Perturbations
H = H_0 + ?H
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
S_mean = s/Sqrt[N]
? exp(-e/t)

49. Magnetic field due to a segment of wire
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Always Real
Cv = dE/dT = 3R
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

50. EM: Series Capacitance
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)
? exp(-e/t)
C_eq = (? 1/C_i)^-1