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GRE Physics

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Answer 50 questions in 15 minutes.
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1. Relativistic Energy
?mc²
4H + 2e- ? He +2? + 6?
C_eq = (? 1/C_i)^-1
I = I_0 Cos[?]^2

2. Single Slit Diffraction Intensity
V(r) + L²2/2mr²
X_L = X_C or X_total = 0
Exp(N(µ-e)/t)
I = Im (sinc²(a)) ; a = pai sin(?) / ?

3. Source-free RC Circuit
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Hbar*?³/(p²c³exp(hbar?/t)-1)
X_L = i?L
L = T - V dL/dq = d/dt dL/dqdot

4. Hall Coefficient
1/ne - where n is charge carrier density
<T> = -<V>/2
1/2 CV²
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

5. Perpendicular axis theorem
v(mean)
I_z = I_x + I_y (think hoop symmetry)
Z²/n² (m_red/m_elec)
ma + kx = 0

6. Stark Effect
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
B = µ0 I n
DW/dq
Q = CVexp(-t/RC)

7. EM: Series Capacitance
V(r) + L²2/2mr²
C_eq = (? 1/C_i)^-1
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
?mv

8. Self Inductance
S_mean = s/Sqrt[N]
V = -L di/dt
F = mv²/r
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

9. Virial Theorem
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
?~1/T
<T> = 1/2 * <dV/dx>
F = R/2

10. Internal Energy of an Ideal Gas
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Z_c = -i/(?C) ; Z_L = i ? L
(3/2) n R ?t
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

11. Lensmaker Equation - Thin Lens
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
I = I_cm + (1/2)m d^2
V(r) + L²2/2mr²

12. EM: Maxwell'S equations
E²-p²c²
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
<?|O|?>

13. Thin Film Theory: Constructive / Destructive Interference
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.
H = H_0 + ?H
DS = 0 - dQ = 0 - P V^? = constant
Const: 2t = (n +.5)? Destructive 2t = n?

14. Thermo: Blackbody Radiation
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
NC?T
F = s * T4
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

15. Boltzmann / Canonical distribution
J = E s - s = Conductivity - E = Electric field
F = f* (c+v_r)/(c+v_s)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

16. td(entropy) =
X_C = 1/(i?C)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Faraday/Lenz: current inducted opposes the changing field
PdV +dU

17. EM: Reactance of Inductor
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
I ' = I cos²(?)
X_L = i?L

18. Malus Law

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19. Heat added
P/A = s T^4
F = -2*m(? x r)
NC?T
Q = CVexp(-t/RC)

20. Force exerted on charge by long wire
E = <?| H |?>
F = µ0 q v I / 2pr
DW/dq
Q = CVexp(-t/RC)

21. A reversible process stays..
? = 5/3
Infinitely close to equilibrium at all times
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
dQ = dW +dU

22. How to derive cylcotron frequency
qvb = mv²/R
P² ~ R³
F = µ0 q v I / 2pr
(3/2) n R ?t

23. Energy levels from the Coulomb potential
F = qv×B
<?1|?2> = 0 ? Orthogonal
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
J/(ne) n: atom density

24. SR: Total Energy of a Particle
?~T
µ0 I / 2pR
ma + kx = 0
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

25. E field of a capacitor (d->0)
E = s/e_0
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
P1V1 - P2V2 / (? - 1)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

26. Partition Function
? exp(-e/t)
? = 5/3
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Exp(N(µ-e)/t)

27. Quant: Orthogonality of States
Const: 2t = (n +.5)? Destructive 2t = n?
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
<?1|?2> = 0 ? Orthogonal
1/ne - where n is charge carrier density

28. Astro: Aperture Formula (Rayleigh Criterion)
? = 1.22? / d
? = 1.22?/D
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Asin(?) = m?

29. First law of thermodynamics (explain direction of energy for each term)
µ0 I / 2R
.5 LI²
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
I = I_cm + md²

30. Bernoulli Equation
.5 LI²
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
P +1/2 ? v² + ?gh = Constant
? = 5/3

31. Magnetic Field For Current in Long Wire
B = µ0 I n
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
E²-p²c²
µ0 I / 2pR

32. De Broigle Wavelength
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
T = I?²/2
? = h/mv
Infinitely close to equilibrium at all times

33. QM: de Broglie Wavelength
F = µ0 q v I / 2pr
V = -L di/dt
µ=s^2
?= h/v(2mE)

34. Magnetic field due to a segment of wire
dU = 0 ? dS = ?dW/T
Always Real
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
A[B -C] + [A -C]B

35. Thermo: 1st Law
ds² = (c*dt)² - ?(x_i)²
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.
dQ = dW +dU
T^2 = k R^3 - k=constant

36. Atom: Orbital Config
µ0 I1I2 / (2pd)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
J = E s - s = Conductivity - E = Electric field
DW = P dV

37. Single Slit Diffraction Maximum
Asin(?) = m?
(° of Freedom)kT/2
B = µ0 I n
I = I_cm + md²

38. Mech: Force of Friction
Exp(N(µ-e)/t)
µ = Current * Area T = µ x B
F_f = µ*F_N
V = V0 + V0 a ?T

39. Magnetic Field of a long solenoid
B = µ0 I n
X_L = X_C or X_total = 0
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
1/ne - where n is charge carrier density

40. Kepler'S third law (T and R)
T^2 = k R^3 - k=constant
E = <?| H |?>
L = mr²d?/dt
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

41. Rotation matrix (2x2)
Sin(?) = ?/d
dU = 0 ? dS = ?dW/T
Cos[?] Sin[?] -Sin[?] Cos[?]
F_f = µ*F_N

42. EM: Parallel Capacitance
C_eq = ?C_i
.5 CV²
Braking Radiation
Sin(?) = ?/d

43. Quant: Commutator Relation [AB -C]
?~1/T
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
A[B -C] + [A -C]B
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

44. Rayleigh criterion
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
µ = m_e/2
I = I_cm + md²
? = 1.22? / d

45. Quant: Eigenvalue of Hermitian Operator
? = 5/3
Always Real
A[B -C] + [A -C]B
J/(ne) n: atom density

46. Magnetic Field Through Ring
Faraday/Lenz: current inducted opposes the changing field
u dm/dt
S_mean = s/Sqrt[N]
µ0 I / 2R

47. Wein'S displacement law for blackbodies (? and T)
V(r) + L²2/2mr²
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
NC?T
?_max = b/T

48. Radiation (Larmor - and another neat fact)
(° of Freedom)kT/2
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
I ' = I cos²(?)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

49. Springs in series/parallel
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
P1V1 - P2V2 / (? - 1)
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
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

50. Parallel axis theorem
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
F = qv×B
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
I = I_cm + (1/2)m d^2

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