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GRE Physics

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. A reversible process stays..
V = -L di/dt
Infinitely close to equilibrium at all times
Dp/dt = L / (t ?V)
?= h/v(2mE)

2. Kepler'S third law (T and R)
Const: 2t = (n +.5)? Destructive 2t = n?
.5 CV²
T^2 = k R^3 - k=constant
V(r) + L²2/2mr²

3. Mean electron drift speed
J = ? Fdt
N²/Z (m_elec/m_red)
J/(ne) n: atom density
?mv

4. Mech: Force of Friction
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
C_eq = ?C_i
F_f = µ*F_N
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.

5. Addition of relativistic velocities

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6. Rocket Thrust
F = µ0 q v I / 2pr
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
u dm/dt
Cv = dE/dT = 3R

7. Angular momentum operators L^2 and L_z
?s = 0 - ?l = ±1
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
F = s * T4

8. Double Slit: Interference Minimum - Diffraction Minimum
B = µ0 I n
?max = 2.898 x 10 -³ / T
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
µ0 I1I2 / (2pd)

9. EM: Bremsstrahlung (translation)
Braking Radiation
? = h/mv
F = mv²/r
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

10. Thermo: Isothermal
dU = 0 ? dS = ?dW/T
A[B -C] + [A -C]B
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Sin(?) = ?/d

11. Inductance of Solenoid
?max = 2.898 x 10 -³ / T
u dm/dt
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

12. SR: Spacetime Interval
M? = 2dsin(?)
ds² = (c*dt)² - ?(x_i)²
Ct²-x²-y²-z²
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

13. Energy in Inductor
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
µ = m_e/2
V = -L di/dt
.5 LI²

14. Doppler Shift for light
? = ?0 root((1-v/c)/(1+v/c))
L = T - V dL/dq = d/dt dL/dqdot
? = h/mv
? (t-vx/c²)

15. Triplet/singlet states: symmetry and net spin
0
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
J/(ne) n: atom density
DW = P dV

16. E field of a capacitor (d->0)
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
J = E s - s = Conductivity - E = Electric field
E = s/e_0
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

17. EM: Method of Images
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Opposing charge induced upon conductor
C_eq = (? 1/C_i)^-1
X_L = i?L

18. QM: de Broglie Wavelength
?= h/v(2mE)
?~T
<?|O|?>
F = f* (c+v_r)/(c+v_s)

19. Thermo: Monatomic gas ?=?
P +1/2 ? v² + ?gh = Constant
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
? = 5/3
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

20. Quant: Orthogonality of States
Hbar*?³/(p²c³exp(hbar?/t)-1)
?= h/v(2mE)
C_eq = (? 1/C_i)^-1
<?1|?2> = 0 ? Orthogonal

21. Coriolis Force
X_C = 1/(i?C)
Q = CVexp(-t/RC)
Hbar*?³/(p²c³exp(hbar?/t)-1)
F = -2*m(? x r)

22. Adiabatic processes (dS - dQ - P and V)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
DS = 0 - dQ = 0 - P V^? = constant
Measurements close to true value
1/vLC

23. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Asin(?) = m?
µ = m_e/2
F = s * T4

24. Malus Law

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25. Perturbations
E = Z²*E1
µ=s^2
H = H_0 + ?H
P/A = s T^4

26. Current in resistor in RC circuit
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
U = t^2 d/dt (logZ)
I = V/R exp(-t/RC)

27. Pauli matrices
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/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
F = R/2

28. Atom: Positronium Reduced Mass
Braking Radiation
F = s * T4
H = H_0 + ?H
µ = m_e/2

29. Astro: Aperture Formula (Rayleigh Criterion)
? = 1.22?/D
? (t-vx/c²)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
A[B -C] + [A -C]B

30. Work done on a gas
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Isentropic
DW = P dV
X_C = 1/(i?C)

31. Polarizers - intensity when crossed at ?
I = I_0 Cos[?]^2
0
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
? = 5/3

32. Clausius-Clapeyron Equation
Cv = dE/dT = 3R
V = -L di/dt
Dp/dt = L / (t ?V)
v(mean)

33. Lagrangian and Lagrange'S equation
L = T - V dL/dq = d/dt dL/dqdot
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
F = s * T4

34. Complex impedance (expressions for capacitor and inductor)
Z_c = -i/(?C) ; Z_L = i ? L
Cos[?] Sin[?] -Sin[?] Cos[?]
N²/Z (m_elec/m_red)
U - ts = -tlog(Z)

35. Resistance - length - area - rho
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
F = I L X B
KE = 1/2 * µ (dr/dt)² L = µ r x v

36. How to derive cylcotron frequency
I = Im (sinc²(a)) ; a = pai sin(?) / ?
qvb = mv²/R
Measurements close to mean
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

37. Partition Function
L = L_0 Sqrt[1-v^2/c^2]
ds² = (c*dt)² - ?(x_i)²
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
? exp(-e/t)

38. Mech: Virial Theorem
Isentropic
Always Real
<T> = -<V>/2
Braking Radiation

39. Thermo: 1st Law
Braking Radiation
dQ = dW +dU
A[B -C] + [A -C]B
PdV +dU

40. Bernoulli Equation
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
C_eq = (? 1/C_i)^-1
P +1/2 ? v² + ?gh = Constant
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

41. Kepler'S Three Laws
µ=s^2
H = H_0 + ?H
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

42. Bohr Model: Energy
Z²/n² (m_red/m_elec)
Ct²-x²-y²-z²
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.
L = T - V dL/dq = d/dt dL/dqdot

43. Time Lorentz Transformation
Measurements close to true value
C = 4pe0 ab/(a-b) = inner and outer radii
? (t-vx/c²)
(3/2) n R ?t

44. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
u dm/dt
X_L = i?L
NC?T

45. EM: Maxwell'S equations
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
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
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

46. Selection Rules
?~1/T
?s = 0 - ?l = ±1
Cos[?] Sin[?] -Sin[?] Cos[?]
µ0 I / 2pR

47. Energy in a Capacitor
E = <?| H |?>
J/(ne) n: atom density
.5 CV²
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

48. Effective Potential
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
V(r) + L²2/2mr²
Dv = -udm/m - v = v0 + u ln(m0/m)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

49. Error in the mean if each measurement has the same uncertainty s
L = mr²d?/dt
S_mean = s/Sqrt[N]
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

50. Wein'S Displacement Law
?~1/T
F = f* (c+v_r)/(c+v_s)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
?max = 2.898 x 10 -³ / T