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GRE Physics

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Answer 50 questions in 15 minutes.
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1. EM: Maxwell'S equations
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^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)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
J/(ne) n: atom density

2. Force on a wire in magnetic field
F = I L X B
<T> = 1/2 * <dV/dx>
Ct²-x²-y²-z²
I = V/R exp(-t/RC)

3. Lab: Precision of Measurements
(° of Freedom)kT/2
? = 5/3
ds² = (c*dt)² - ?(x_i)²
Measurements close to mean

4. Bernoulli Equation
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
P +1/2 ? v² + ?gh = Constant
µ0 I / 2R
T^2 = k R^3 - k=constant

5. EM: SHO (Hooke)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
I = I_cm + (1/2)m d^2
Sin(?) = ?/d
ma + kx = 0

6. Perturbations
DW/dq
L = T - V dL/dq = d/dt dL/dqdot
H = H_0 + ?H
C_eq = ?C_i

7. Atom: Bohr Formula
P/A = s T^4
V = V0 + V0 a ?T
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
µ0 I / 2R

8. Focal point of mirrror with curvature
V(r) + L²2/2mr²
u dm/dt
F = R/2
E = <?| H |?>

9. Source Free RL Circuit
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
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
T^2 = k R^3 - k=constant
C = 4pe0 ab/(a-b) = inner and outer radii

10. Atom: Hydrogen Wave Function Type
?max = 2.898 x 10 -³ / T
?s = 0 - ?l = ±1
Exponentially decreasing radial function
Z_c = -i/(?C) ; Z_L = i ? L

11. td(entropy) =
I = Im (sinc²(a)) ; a = pai sin(?) / ?
PdV +dU
Exp(N(µ-e)/t)
v(mean)

12. Stark Effect
1/ne - where n is charge carrier density
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
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
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

13. Biot-Savart law
Z = ?g_i*exp(-E/kT)
Dp/dt = L / (t ?V)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
? = h/p

14. Solid: Resistivity of Metal
V = -L di/dt
?~T
ih_barL_z
dQ = dW +dU

15. EM: AC Resonance
X_L = X_C or X_total = 0
?s = 0 - ?l = ±1
Z²/n² (m_red/m_elec)
Const: 2t = (n +.5)? Destructive 2t = n?

16. Source-free RC Circuit
T^2 = k R^3 - k=constant
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
? = 1.22?/D
<T> = 1/2 * <dV/dx>

17. Single Slit Diffraction Intensity
Dp/dt = L / (t ?V)
Opposing charge induced upon conductor
I = Im (sinc²(a)) ; a = pai sin(?) / ?
L = L_0 Sqrt[1-v^2/c^2]

18. Lagrangian and Lagrange'S equation
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
L = T - V dL/dq = d/dt dL/dqdot
.5 LI²
I = I_0 Cos[?]^2

19. Rotation matrix (2x2)
I ' = I cos²(?)
L = L_0 Sqrt[1-v^2/c^2]
Cos[?] Sin[?] -Sin[?] Cos[?]
I = -(c ?t)^2 + d^2

20. Magnetic field due to a segment of wire
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
Q = CVexp(-t/RC)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
<?|O|?>

21. De Broigle Wavelength
X_L = X_C or X_total = 0
? = h/mv
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
µ0 I1I2 / (2pd)

22. Solid: Resistivity of Semi-Conductor
N²/Z (m_elec/m_red)
F = R/2
?~1/T
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. Rayleigh'S Criterion
0
?mc²
Sin(?) = ?/d
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

24. Anomalous Zeeman Effect

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25. Magnetic Dipole Moment and Torque
µ = Current * Area T = µ x B
T^2 = k R^3 - k=constant
B = µ0 I n
Always Real

26. Kepler'S Three Laws
? exp(-e/t)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
1/vLC

27. First law of thermodynamics (explain direction of energy for each term)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
4H + 2e- ? He +2? + 6?
Exp(N(µ-e)/t)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

28. Gibbs Factor
Measurements close to true value
?~1/T
I = V/R exp(-t/RC)
Exp(N(µ-e)/t)

29. Mech: Rotational Energy
Infinitely close to equilibrium at all times
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
T = I?²/2
E = <?| H |?>

30. Thermo: Partition Function
DW/dq
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Z = ?g_i*exp(-E/kT)
P/A = s T^4

31. Time Lorentz Transformation
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
? (t-vx/c²)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

32. Inductance of Solenoid
?mc²
4H + 2e- ? He +2? + 6?
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

33. Selection rules for atomic transitions
P +1/2 ? v² + ?gh = Constant
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
J = E s - s = Conductivity - E = Electric field
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

34. Radiation (Larmor - and another neat fact)
V = -L di/dt
KE = 1/2 * µ (dr/dt)² L = µ r x v
ds² = (c*dt)² - ?(x_i)²
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

35. Heat added
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
NC?T
µ0 I1I2 / (2pd)
I ' = I cos²(?)

36. Dulong Petit Law
X_C = 1/(i?C)
Cv = dE/dT = 3R
U - ts = -tlog(Z)
V = -L di/dt

37. Virial Theorem
<T> = 1/2 * <dV/dx>
V = -L di/dt
Braking Radiation
I ' = I cos²(?)

38. Mech: Virial Theorem
<T> = -<V>/2
? exp(-e/t)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Infinitely close to equilibrium at all times

39. Angular momentum operators L^2 and L_z
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
<T> = -<V>/2
DW = P dV
J/(ne) n: atom density

40. Expectation value of the energy of state |?>
<T> = -<V>/2
S = k ln[O] ; dS = dQ/T
E = <?| H |?>
<T> = 1/2 * <dV/dx>

41. Thermo: Blackbody Radiation
J = ? Fdt
F = s * T4
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
<?1|?2> = 0 ? Orthogonal

42. Thermo: 1st Law
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
dQ = dW +dU
µ0 I / 2R
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

43. EM: Series Capacitance
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
C_eq = (? 1/C_i)^-1
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

44. De Broglie wavelength
<T> = 1/2 * <dV/dx>
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
F = I L X B
? = h/p

45. Astro: Kepler'S Third Law
Hbar*?³/(p²c³exp(hbar?/t)-1)
A[B -C] + [A -C]B
P² ~ R³
I = V/R exp(-t/RC)

46. Angular momentum - Central Force Motion
P/A = s T^4
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
?~T
L = mr²d?/dt

47. EM: Parallel Capacitance
F = f* (c+v_r)/(c+v_s)
C_eq = ?C_i
X_L = X_C or X_total = 0
(3/2) n R ?t

48. Resonance frequency of LC circuit
S = k ln[O] ; dS = dQ/T
C = 4pe0 ab/(a-b) = inner and outer radii
1/vLC
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

49. Magnetic Field Through Ring
Dv = -udm/m - v = v0 + u ln(m0/m)
Q = CVexp(-t/RC)
µ = m_e/2
µ0 I / 2R

50. Relativistic Energy
P +1/2 ? v² + ?gh = Constant
Isentropic
?mc²
I = I_cm + md²

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