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GRE Physics

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Answer 50 questions in 15 minutes.
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1. Source-free RC Circuit
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
V = V0 + V0 a ?T
µ0 I1I2 / (2pd)

2. De Broglie wavelength
?_max = b/T
1/ne - where n is charge carrier density
? = h/p
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

3. Delta Function Potential - type of WF
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
? = 1.22? / d
0

4. Kepler'S third law (T and R)
L = mr²d?/dt
?mv
Faraday/Lenz: current inducted opposes the changing field
T^2 = k R^3 - k=constant

5. Resistance - length - area - rho
µ = Current * Area T = µ x B
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
C_eq = (? 1/C_i)^-1

6. Magnetic Field of a long solenoid
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
B = µ0 I n
µ0 I / 2R
V = -L di/dt

7. Thermo: Monatomic gas ?=?
?mv
Cos[?] Sin[?] -Sin[?] Cos[?]
P1V1 - P2V2 / (? - 1)
? = 5/3

8. Polarizers - intensity when crossed at ?
F = s * T4
L = T - V dL/dq = d/dt dL/dqdot
J/(ne) n: atom density
I = I_0 Cos[?]^2

9. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
X_L = i?L
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

10. Internal Energy of an Ideal Gas
F = qv×B
? = h/p
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
(3/2) n R ?t

11. Stoke'S Theorem
B = µ0 I n
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
F = µ0 q v I / 2pr
Int ( A . dr) = Int ( del x A) dSurface

12. Source Free RL Circuit
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
T = I?²/2
I = I_cm + (1/2)m d^2

13. Adiabatic processes (dS - dQ - P and V)
H = H_0 + ?H
U - ts = -tlog(Z)
DS = 0 - dQ = 0 - P V^? = constant
? = h/p

14. Partition Function
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
1/ne - where n is charge carrier density
? exp(-e/t)
?mv

15. EM: SHO (Hooke)
µ0 I1I2 / (2pd)
ma + kx = 0
µ=s^2
F = I L X B

16. Hamiltonian and Hamilton'S equations
X_C = 1/(i?C)
Hbar*?³/(p²c³exp(hbar?/t)-1)
S_mean = s/Sqrt[N]
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

17. Selection Rules
µ0 I1I2 / (2pd)
?s = 0 - ?l = ±1
Opposing charge induced upon conductor
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

18. Malus Law

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19. EM: Electromagnetic inertia
Faraday/Lenz: current inducted opposes the changing field
F = qv×B
U - ts = -tlog(Z)
0

20. Volumetric Expansion
v(mean)
u dm/dt
V = V0 + V0 a ?T
?mv

21. Bar magnets -- direction of B field lines - earth'S B field
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Asin(?) = m?
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

22. Magnetic Field Through Ring
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
X_C = 1/(i?C)
µ0 I / 2R
Infinitely close to equilibrium at all times

23. RLC resonance condition
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
I = V/R exp(-t/RC)
dQ = dW +dU
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

24. Thermo: Adiabatic Work vs Isothermal Work
W_A < W_I
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
P1V1 - P2V2 / (? - 1)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

25. Mech: Force of Friction
µ = m_e/2
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
F_f = µ*F_N

26. Wein'S displacement law for blackbodies (? and T)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
?_max = b/T
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
<T> = -<V>/2

27. Rocket Equation
Dv = -udm/m - v = v0 + u ln(m0/m)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Sin(?) = ?/d
N²/Z (m_elec/m_red)

28. Relativistic Energy
F_f = µ*F_N
?mc²
X_C = 1/(i?C)
L = T - V dL/dq = d/dt dL/dqdot

29. SR: Total Energy of a Particle
V(r) + L²2/2mr²
1/vLC
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
<?1|?2> = 0 ? Orthogonal

30. Lab: Standard Deviation of Poisson
v(mean)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
C = 4pe0 ab/(a-b) = inner and outer radii
Faraday/Lenz: current inducted opposes the changing field

31. Time Lorentz Transformation
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
1/vLC
?~1/T
? (t-vx/c²)

32. Anomalous Zeeman Effect

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33. Error in the mean if each measurement has the same uncertainty s
S_mean = s/Sqrt[N]
V(r) + L²2/2mr²
I = I_cm + (1/2)m d^2
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.

34. Resonance frequency of LC circuit
NC?T
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Q = CVexp(-t/RC)
1/vLC

35. Relativistic Momentum
N d flux / dt
?mv
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Const: 2t = (n +.5)? Destructive 2t = n?

36. Lensmaker Equation - Thin Lens
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
ds² = (c*dt)² - ?(x_i)²
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

37. Inductance of Solenoid
µ0 I / 2pR
H = H_0 + ?H
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
? = 1.22?/D

38. Rocket Thrust
u dm/dt
T = I?²/2
<T> = -<V>/2
M? = 2dsin(?)

39. Virial Theorem
<T> = 1/2 * <dV/dx>
F = mv²/r
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.
ds² = (c*dt)² - ?(x_i)²

40. Selection rules for atomic transitions
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
?max = 2.898 x 10 -³ / T
C = 4pe0 ab/(a-b) = inner and outer radii

41. Coriolis Force
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
E²-p²c²
F = -2*m(? x r)
Faraday/Lenz: current inducted opposes the changing field

42. Induced EMF of solenoid
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
F = I L X B
N d flux / dt
Ct²-x²-y²-z²

43. Magnetic Field For Current in Long Wire
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
µ0 I / 2pR
.5 LI²
µ = m_e/2

44. EM: Maxwell'S equations
Measurements close to mean
u dm/dt
E = <?| H |?>
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

45. Boltzmann / Canonical distribution
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
F = f* (c+v_r)/(c+v_s)
? = h/p
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

46. Kepler'S Three Laws
1/ne - where n is charge carrier density
I ' = I cos²(?)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Int ( A . dr) = Int ( del x A) dSurface

47. EM: Parallel Capacitance
C_eq = ?C_i
?max = 2.898 x 10 -³ / T
1/ne - where n is charge carrier density
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

48. Atom: Bohr Theory Ionization
? = 1.22? / d
E = Z²*E1
v(mean)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

49. Force on a wire in magnetic field
U - ts = -tlog(Z)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
F_f = µ*F_N
F = I L X B

50. Bohr Model: Radii
J/(ne) n: atom density
N²/Z (m_elec/m_red)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
DW = P dV

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