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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
4H + 2e- ? He +2? + 6?
F = qv×B
ds² = (c*dt)² - ?(x_i)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)

2. Mech: Rotational Energy
F = µ0 q v I / 2pr
(° of Freedom)kT/2
T = I?²/2
Sin(?) = ?/d

3. Energy in terms of partition function
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.
E = <?| H |?>
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
U = t^2 d/dt (logZ)

4. Electromotive Force
P/A = s T^4
DW/dq
1/vLC
T^2 = k R^3 - k=constant

5. Force exerted on charge by long wire
P1V1 - P2V2 / (? - 1)
Z_c = -i/(?C) ; Z_L = i ? L
F = µ0 q v I / 2pr
Dp/dt = L / (t ?V)

6. Delta Function Potential - type of WF
X_L = i?L
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
? = 5/3

7. Induced EMF of solenoid
<?|O|?>
? = 1.22? / d
N d flux / dt
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

8. Virial Theorem
Ct²-x²-y²-z²
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
<T> = 1/2 * <dV/dx>
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

9. Force/length between two wires
ma + kx = 0
µ0 I1I2 / (2pd)
I = -(c ?t)^2 + d^2
F = R/2

10. Single Slit Diffraction Intensity
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Always Real
L = T - V dL/dq = d/dt dL/dqdot
J/(ne) n: atom density

11. A reversible process stays..
Infinitely close to equilibrium at all times
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
dU = 0 ? dS = ?dW/T
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

12. Mech: Parallel Axis Theorem (Moment of Inertia)
µ = Current * Area T = µ x B
1/2 CV²
DS = 0 - dQ = 0 - P V^? = constant
I = I_cm + md²

13. Compton Scattering
E = s/e_0
?max = 2.898 x 10 -³ / T
Const: 2t = (n +.5)? Destructive 2t = n?
?? = h/mc * (1-cos(?))

14. Planck Radiation Law
? = 5/3
Hbar*?³/(p²c³exp(hbar?/t)-1)
1/2 CV²
I = I_cm + md²

15. Rocket Thrust
Braking Radiation
U = t^2 d/dt (logZ)
µ = m_e/2
u dm/dt

16. Hamiltonian and Hamilton'S equations
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
T^2 = k R^3 - k=constant
? (t-vx/c²)

17. Effective Potential
V(r) + L²2/2mr²
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)
L = mr²d?/dt

18. EM: SHO (Hooke)
NC?T
ma + kx = 0
Infinitely close to equilibrium at all times
Dv = -udm/m - v = v0 + u ln(m0/m)

19. EM: Reactance of Capacitor
X_C = 1/(i?C)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
? = h/mv
B = µ0 I n

20. Thermo: Blackbody Radiation
Ct²-x²-y²-z²
F = s * T4
F = -2*m(? x r)
<T> = -<V>/2

21. Time Lorentz Transformation
? (t-vx/c²)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
I = V/R exp(-t/RC)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

22. Magnetic field due to a segment of wire
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Asin(?) = m?
I ' = I cos²(?)
I = V/R exp(-t/RC)

23. 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)
KE = 1/2 * µ (dr/dt)² L = µ r x v
Measurements close to true value
1/vLC

24. Partition Function
Exp(N(µ-e)/t)
B = µ0 I n
? exp(-e/t)
? = h/mv

25. Astro: Aperture Formula (Rayleigh Criterion)
? = 1.22?/D
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Measurements close to true value
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

26. Thermo: Adiabatic Work vs Isothermal Work
F = µ0 q v I / 2pr
W_A < W_I
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

27. EM: AC Resonance
X_L = X_C or X_total = 0
V = -L di/dt
µ = m_e/2
J = E s - s = Conductivity - E = Electric field

28. Invariant Energy Quantity
F = s * T4
E²-p²c²
µ0 I / 2R
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

29. Error in the mean if each measurement has the same uncertainty s
V = V0 + V0 a ?T
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
S_mean = s/Sqrt[N]
Cos[?] Sin[?] -Sin[?] Cos[?]

30. Thermo: Monatomic gas ?=?
? = 5/3
I ' = I cos²(?)
Z = ?g_i*exp(-E/kT)
?~T

31. Work done on a gas
E = Z²*E1
DW = P dV
Dp/dt = L / (t ?V)
W_A < W_I

32. Current in resistor in RC circuit
?~1/T
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Isentropic
I = V/R exp(-t/RC)

33. Malus Law

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34. Magnetic Field For Current in Long Wire
? = h/p
? = 1.22?/D
B = µ0 I n
µ0 I / 2pR

35. Rocket Equation
<?|O|?>
Dv = -udm/m - v = v0 + u ln(m0/m)
dU = 0 ? dS = ?dW/T
T^2 = k R^3 - k=constant

36. Adiabatic means
N²/Z (m_elec/m_red)
Isentropic
Infinitely close to equilibrium at all times
F = I L X B

37. Thermo: Average Total Energy
?= h/v(2mE)
ma + kx = 0
(° of Freedom)kT/2
?~1/T

38. td(entropy) =
PdV +dU
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Opposing charge induced upon conductor
(° of Freedom)kT/2

39. Triplet/singlet states: symmetry and net spin
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
F = -2*m(? x r)
P1V1 - P2V2 / (? - 1)
Braking Radiation

40. EM: Method of Images
Opposing charge induced upon conductor
.5 CV²
I = V/R exp(-t/RC)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

41. Volumetric Expansion
Dv = -udm/m - v = v0 + u ln(m0/m)
µ0 I / 2R
V = V0 + V0 a ?T
A[B -C] + [A -C]B

42. Lagrangian and Lagrange'S equation
E = Z²*E1
? = h/mv
L = T - V dL/dq = d/dt dL/dqdot
µ0 I1I2 / (2pd)

43. EM: Bremsstrahlung (translation)
? (t-vx/c²)
<?1|?2> = 0 ? Orthogonal
Braking Radiation
I = I_cm + md²

44. Rotation matrix (2x2)
Cos[?] Sin[?] -Sin[?] Cos[?]
E = Z²*E1
Always Real
v(mean)

45. Mech: Force of Friction
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
X_C = 1/(i?C)
F_f = µ*F_N

46. Inductance of Solenoid
E²-p²c²
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Exponentially decreasing radial function
S_mean = s/Sqrt[N]

47. Quant: Expectation Value
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 = mr²d?/dt
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
<?|O|?>

48. Bar magnets -- direction of B field lines - earth'S B field
Q = CVexp(-t/RC)
Sin(?) = ?/d
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

49. Thermo: 1st Law
dQ = dW +dU
Measurements close to mean
Measurements close to true value
F = f* (c+v_r)/(c+v_s)

50. Atom: Bohr Theory Ionization
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
E = Z²*E1
DW/dq
J/(ne) n: atom density

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