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GRE Physics

Instructions:

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. Magnetic field due to a segment of wire
<?|O|?>
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Dp/dt = L / (t ?V)
P² ~ R³

2. EM: Bremsstrahlung (translation)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Braking Radiation
C_eq = ?C_i
µ0 I / 2pR

3. Work done on a gas
1/2 CV²
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
DW = P dV
v(mean)

4. Astro: Kepler'S Third Law
.5 LI²
ma + kx = 0
C_eq = (? 1/C_i)^-1
P² ~ R³

5. Ohm'S Law w/ current density
F = -2*m(? x r)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
1/vLC
J = E s - s = Conductivity - E = Electric field

6. Invariant spatial quantity
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
(3/2) n R ?t
Ct²-x²-y²-z²

7. Center of Mass: Kinetic Energy & Angular Momentum
U = t^2 d/dt (logZ)
KE = 1/2 * µ (dr/dt)² L = µ r x v
F = mv²/r
J = E s - s = Conductivity - E = Electric field

8. Polarizers - intensity when crossed at ?
I = I_0 Cos[?]^2
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

9. Relativistic Momentum
I = I_cm + md²
?mv
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
?~1/T

10. Mech: Force of Friction
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Z_c = -i/(?C) ; Z_L = i ? L
F_f = µ*F_N
N d flux / dt

11. Energy in terms of partition function
T = I?²/2
u dm/dt
Infinitely close to equilibrium at all times
U = t^2 d/dt (logZ)

12. Parallel axis theorem
I = I_cm + (1/2)m d^2
Asin(?) = m?
F = µ0 q v I / 2pr
ma + kx = 0

13. Malus Law

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14. Relativistic Energy
Always Real
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Sin(?) = ?/d
?mc²

15. Quant: Orthogonality of States
?mv
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
<?1|?2> = 0 ? Orthogonal
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

16. Electromotive Force
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
DW/dq
1/2 CV²
W_A < W_I

17. Lab: Standard Deviation of Poisson
v(mean)
Int ( A . dr) = Int ( del x A) dSurface
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
? (t-vx/c²)

18. Solid: Resistivity of Semi-Conductor
C_eq = (? 1/C_i)^-1
?~1/T
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
V = -L di/dt

19. EM: SHO (Hooke)
ma + kx = 0
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
?mv
Dv = -udm/m - v = v0 + u ln(m0/m)

20. Internal Energy of an Ideal Gas
(° of Freedom)kT/2
(3/2) n R ?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
µ0 I / 2pR

21. Kepler'S third law (T and R)
Hbar*?³/(p²c³exp(hbar?/t)-1)
T^2 = k R^3 - k=constant
1/ne - where n is charge carrier density
C_eq = ?C_i

22. Pauli matrices
Measurements close to mean
0
V = -L di/dt
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. EM: Series Capacitance
Braking Radiation
F = -2*m(? x r)
I = I_0 Cos[?]^2
C_eq = (? 1/C_i)^-1

24. Induced EMF of solenoid
(° of Freedom)kT/2
F = qv×B
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
N d flux / dt

25. Time Lorentz Transformation
Isentropic
Cv = dE/dT = 3R
X_L = i?L
? (t-vx/c²)

26. Compton Scattering
4H + 2e- ? He +2? + 6?
?? = h/mc * (1-cos(?))
J/(ne) n: atom density
P1V1 - P2V2 / (? - 1)

27. EM: Lorentz Force
1/2 CV²
?_max = b/T
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
F = qv×B

28. Thermo: Average Total Energy
V = V0 + V0 a ?T
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
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
(° of Freedom)kT/2

29. 3 Laws of Thermo
NC?T
DS = 0 - dQ = 0 - P V^? = constant
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
U - ts = -tlog(Z)

30. Lagrangian and Lagrange'S equation
L = T - V dL/dq = d/dt dL/dqdot
?~T
Exponentially decreasing radial function
Sin(?) = ?/d

31. Gibbs Factor
F = -2*m(? x r)
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
Exp(N(µ-e)/t)
J/(ne) n: atom density

32. Magnetic Field Through Ring
µ0 I / 2R
? = ?0 root((1-v/c)/(1+v/c))
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
F = mv²/r

33. Lab: Accuracy of Measurements
Measurements close to true value
?_max = b/T
P1V1 - P2V2 / (? - 1)
Braking Radiation

34. Quant: Eigenvalue of Hermitian Operator
?mc²
Always Real
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
T^2 = k R^3 - k=constant

35. QM: de Broglie Wavelength
?= h/v(2mE)
? = ?0 root((1-v/c)/(1+v/c))
Const: 2t = (n +.5)? Destructive 2t = n?
F = f* (c+v_r)/(c+v_s)

36. Atom: Bohr Theory Ionization
E = Z²*E1
A[B -C] + [A -C]B
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
F = -2*m(? x r)

37. Stefan-Boltzmann law for blackbodies (power per area and T)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
P/A = s T^4
DS = 0 - dQ = 0 - P V^? = constant
I = -(c ?t)^2 + d^2

38. Helmholtz Free Energy
? = 5/3
Exponentially decreasing radial function
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
U - ts = -tlog(Z)

39. Spherical Capacitor Equation
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Measurements close to true value
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
C = 4pe0 ab/(a-b) = inner and outer radii

40. Triplet/singlet states: symmetry and net spin
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Z = ?g_i*exp(-E/kT)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Int ( A . dr) = Int ( del x A) dSurface

41. Inductance of Solenoid
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
dU = 0 ? dS = ?dW/T

42. Energy levels from the Coulomb potential
1/2 CV²
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
qvb = mv²/R
?s = 0 - ?l = ±1

43. Expectation value of the energy of state |?>
W_A < W_I
C_eq = ?C_i
E = <?| H |?>
V = -L di/dt

44. Clausius-Clapeyron Equation
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
A[B -C] + [A -C]B
Dp/dt = L / (t ?V)
?? = h/mc * (1-cos(?))

45. Source-free RC Circuit
1/ne - where n is charge carrier density
<?1|?2> = 0 ? Orthogonal
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
F = s * T4

46. Anomalous Zeeman Effect

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47. Poisson distribution (µ and s)
I_z = I_x + I_y (think hoop symmetry)
A[B -C] + [A -C]B
DW/dq
µ=s^2

48. Biot-Savart law
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
DW/dq
1/vLC
I = I_cm + (1/2)m d^2

49. SR: Total Energy of a Particle
F = R/2
F = I L X B
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
dU = 0 ? dS = ?dW/T

50. Astro: Aperture Formula (Rayleigh Criterion)
? = 1.22?/D
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
?? = h/mc * (1-cos(?))
Exponentially decreasing radial function