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GRE Physics

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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. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
DW/dq
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
(° of Freedom)kT/2

2. Selection rules for atomic transitions
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
S_mean = s/Sqrt[N]
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

3. Thermo: 1st Law
T^2 = k R^3 - k=constant
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
dQ = dW +dU
M? = 2dsin(?)

4. Addition of relativistic velocities

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5. Relativistic length contraction
L = L_0 Sqrt[1-v^2/c^2]
C_eq = (? 1/C_i)^-1
Dp/dt = L / (t ?V)
Exp(N(µ-e)/t)

6. Wein'S displacement law for blackbodies (? and T)
S = k ln[O] ; dS = dQ/T
?mc²
N²/Z (m_elec/m_red)
?_max = b/T

7. Parallel axis theorem
I_z = I_x + I_y (think hoop symmetry)
I = I_cm + (1/2)m d^2
?mc²
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

8. Magnetic Field Through Ring
Hbar*?³/(p²c³exp(hbar?/t)-1)
µ0 I / 2R
L = mr²d?/dt
DW/dq

9. Stark Effect
ma + kx = 0
L = mr²d?/dt
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
I = I_cm + md²

10. Kepler'S third law (T and R)
T^2 = k R^3 - k=constant
DW/dq
A[B -C] + [A -C]B
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

11. QM: de Broglie Wavelength
DS = 0 - dQ = 0 - P V^? = constant
? = h/mv
?= h/v(2mE)
S_mean = s/Sqrt[N]

12. Force on a wire in magnetic field
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
<?1|?2> = 0 ? Orthogonal
F = I L X B
L = L_0 Sqrt[1-v^2/c^2]

13. Invariant spatial quantity
J = ? Fdt
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Ct²-x²-y²-z²
DS = 0 - dQ = 0 - P V^? = constant

14. Helmholtz Free Energy
I_z = I_x + I_y (think hoop symmetry)
Int ( A . dr) = Int ( del x A) dSurface
I ' = I cos²(?)
U - ts = -tlog(Z)

15. Charge in Capacitor
Q = CVexp(-t/RC)
F = mv²/r
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.
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

16. EM: Series Capacitance
C_eq = (? 1/C_i)^-1
J/(ne) n: atom density
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
? = 1.22? / d

17. Energy in a Capacitor
I = I_cm + md²
.5 CV²
I = Im (sinc²(a)) ; a = pai sin(?) / ?
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

18. Energy in Inductor
L = T - V dL/dq = d/dt dL/dqdot
.5 LI²
C_eq = ?C_i
E²-p²c²

19. Adiabatic processes (dS - dQ - P and V)
F_f = µ*F_N
Exp(N(µ-e)/t)
DS = 0 - dQ = 0 - P V^? = constant
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

20. Current in resistor in RC circuit
?s = 0 - ?l = ±1
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
I = V/R exp(-t/RC)
<T> = -<V>/2

21. Angular momentum - Central Force Motion
I = I_cm + md²
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
L = mr²d?/dt
dQ = dW +dU

22. Rayleigh criterion
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
? = 1.22? / d
dU = 0 ? dS = ?dW/T
W_A < W_I

23. Partition Function
µ0 I1I2 / (2pd)
S_mean = s/Sqrt[N]
?? = h/mc * (1-cos(?))
? exp(-e/t)

24. Center of Mass: Kinetic Energy & Angular Momentum
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
KE = 1/2 * µ (dr/dt)² L = µ r x v
F = qv×B
J = E s - s = Conductivity - E = Electric field

25. Wein'S Displacement Law
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
?max = 2.898 x 10 -³ / T
?_max = b/T
ma + kx = 0

26. Clausius-Clapeyron Equation
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Dp/dt = L / (t ?V)
P1V1 - P2V2 / (? - 1)
?~T

27. Mech: Virial Theorem
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
<T> = -<V>/2

28. Atom: Bohr Formula
qvb = mv²/R
I = I_0 Cos[?]^2
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
1/ne - where n is charge carrier density

29. Magnetic Field of a long solenoid
H = H_0 + ?H
I = I_0 Cos[?]^2
B = µ0 I n
F = -2*m(? x r)

30. Work in a capacitor
1/2 CV²
I = I_cm + (1/2)m d^2
? = h/mv
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

31. Selection Rules
?s = 0 - ?l = ±1
? = 1.22?/D
J/(ne) n: atom density
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

32. Perturbations
H = H_0 + ?H
Cv = dE/dT = 3R
µ0 I / 2R
?max = 2.898 x 10 -³ / T

33. Triplet/singlet states: symmetry and net spin
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
0
H = H_0 + ?H
Asin(?) = m?

34. EM: Electric Field inside of Conductor
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
0
Q = CVexp(-t/RC)
F = -2*m(? x r)

35. Poisson distribution (µ and s)
? = ?0 root((1-v/c)/(1+v/c))
? (t-vx/c²)
Always Real
µ=s^2

36. Relativistic Energy
Dv = -udm/m - v = v0 + u ln(m0/m)
?mc²
dU = 0 ? dS = ?dW/T
I = I_cm + (1/2)m d^2

37. Internal Energy of an Ideal Gas
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.
(3/2) n R ?t
F = R/2
<?|O|?>

38. Boltzmann / Canonical distribution
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
NC?T
A[B -C] + [A -C]B

39. EM: Bremsstrahlung (translation)
Exponentially decreasing radial function
T^2 = k R^3 - k=constant
Braking Radiation
P/A = s T^4

40. Mech: Force of Friction
F_f = µ*F_N
DW = P dV
J = E s - s = Conductivity - E = Electric field
Q = CVexp(-t/RC)

41. 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)
C_eq = ?C_i
.5 LI²
?s = 0 - ?l = ±1

42. Astro: Kepler'S Third Law
N d flux / dt
L = T - V dL/dq = d/dt dL/dqdot
I ' = I cos²(?)
P² ~ R³

43. EM: AC Resonance
X_L = X_C or X_total = 0
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
(° of Freedom)kT/2
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

44. Mech: Parallel Axis Theorem (Moment of Inertia)
I = I_cm + md²
µ0 I / 2pR
F = mv²/r
J = E s - s = Conductivity - E = Electric field

45. Thermo: Blackbody Radiation
? = h/p
J/(ne) n: atom density
Exp(N(µ-e)/t)
F = s * T4

46. Anomalous Zeeman Effect

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47. EM: Lorentz Force
F = qv×B
Sin(?) = ?/d
I = I_cm + md²
NC?T

48. Focal point of mirrror with curvature
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
F = I L X B
F = R/2
? = h/p

49. Malus Law

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50. Gibbs Factor
Exp(N(µ-e)/t)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
v(mean)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

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