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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. Stefan-Boltzmann law for blackbodies (power per area and T)
J = E s - s = Conductivity - E = Electric field
P/A = s T^4
dU = 0 ? dS = ?dW/T
I = I_cm + md²

2. Atom: Orbital Config
µ = Current * Area T = µ x B
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
J = E s - s = Conductivity - E = Electric field
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

3. Magnetic Field Through Ring
µ0 I / 2R
1/ne - where n is charge carrier density
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
F = I L X B

4. Perpendicular axis theorem
(3/2) n R ?t
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.
I_z = I_x + I_y (think hoop symmetry)
E = <?| H |?>

5. A reversible process stays..
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
qvb = mv²/R
? = 1.22? / d
Infinitely close to equilibrium at all times

6. Magnetic Field of a long solenoid
E = <?| H |?>
PdV +dU
B = µ0 I n
<T> = -<V>/2

7. Anomalous Zeeman Effect

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8. Mech: Rotational Energy
F = f* (c+v_r)/(c+v_s)
PdV +dU
T = I?²/2
? = ?0 root((1-v/c)/(1+v/c))

9. How to derive cylcotron frequency
<T> = -<V>/2
qvb = mv²/R
Z = ?g_i*exp(-E/kT)
Int ( A . dr) = Int ( del x A) dSurface

10. Atom: Bohr Formula
?max = 2.898 x 10 -³ / T
M? = 2dsin(?)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
E = Z²*E1

11. Atom: Positronium Reduced Mass
µ = m_e/2
µ0 I / 2R
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
I = V/R exp(-t/RC)

12. Doppler Shift for light
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
? = ?0 root((1-v/c)/(1+v/c))
F = -2*m(? x r)
?? = h/mc * (1-cos(?))

13. Boltzmann / Canonical distribution
DS = 0 - dQ = 0 - P V^? = constant
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
N d flux / dt
F = f* (c+v_r)/(c+v_s)

14. Doppler shift for light
E = <?| H |?>
F_f = µ*F_N
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
?~T

15. Doppler Shift in Frequency
F = f* (c+v_r)/(c+v_s)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
P1V1 - P2V2 / (? - 1)
? = 1.22?/D

16. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
I ' = I cos²(?)
Int ( A . dr) = Int ( del x A) dSurface
J = E s - s = Conductivity - E = Electric field

17. Thermo: Average Total Energy
E = s/e_0
J = E s - s = Conductivity - E = Electric field
(° of Freedom)kT/2
B = µ0 I n

18. Quant: Commutator Relation [AB -C]
v(mean)
A[B -C] + [A -C]B
B = µ0 I n
X_C = 1/(i?C)

19. Mean electron drift speed
J/(ne) n: atom density
Asin(?) = m?
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
I = I_cm + (1/2)m d^2

20. Source Free RL Circuit
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
F = qv×B
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Ct²-x²-y²-z²

21. Inductance of Solenoid
B = µ0 I n
E = s/e_0
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
V(r) + L²2/2mr²

22. EM: Parallel Capacitance
C_eq = ?C_i
Z²/n² (m_red/m_elec)
Int ( A . dr) = Int ( del x A) dSurface
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

23. Thermo: Isothermal
dU = 0 ? dS = ?dW/T
.5 CV²
ma + kx = 0
µ = m_e/2

24. Energy levels from the Coulomb potential
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
0
KE = 1/2 * µ (dr/dt)² L = µ r x v
Measurements close to true value

25. EM: Method of Images
Braking Radiation
Opposing charge induced upon conductor
? = h/p
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

26. Kepler'S third law (T and R)
E = <?| H |?>
.5 CV²
T^2 = k R^3 - k=constant
? exp(-e/t)

27. Current in resistor in RC circuit
Cos[?] Sin[?] -Sin[?] Cos[?]
N²/Z (m_elec/m_red)
I = V/R exp(-t/RC)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

28. Triplet/singlet states: symmetry and net spin
DW/dq
?mv
<?|O|?>
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

29. Expectation value of the energy of state |?>
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
E = <?| H |?>
E = Z²*E1
(3/2) n R ?t

30. EM: Reactance of Capacitor
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
?~1/T
P/A = s T^4
X_C = 1/(i?C)

31. Lab: Precision of Measurements
F = I L X B
Measurements close to mean
I = V/R exp(-t/RC)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

32. Addition of relativistic velocities

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33. Stark Effect
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.
Int ( A . dr) = Int ( del x A) dSurface
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
F = mv²/r

34. First law of thermodynamics (explain direction of energy for each term)
I = I_cm + md²
?~T
Measurements close to true value
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

35. Internal Energy of an Ideal Gas
dQ = dW +dU
(3/2) n R ?t
A[B -C] + [A -C]B
N d flux / dt

36. Thermo: Partition Function
S = k ln[O] ; dS = dQ/T
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.
P +1/2 ? v² + ?gh = Constant
Z = ?g_i*exp(-E/kT)

37. Adiabatic means
B = µ0 I n
Exp(N(µ-e)/t)
Isentropic
F = R/2

38. Weighted average (mean and unc. of mean)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
M? = 2dsin(?)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

39. Dulong Petit Law
Cv = dE/dT = 3R
Measurements close to mean
J = ? Fdt
ds² = (c*dt)² - ?(x_i)²

40. Quant: Orthogonality of States
V(r) + L²2/2mr²
? = h/mv
<?1|?2> = 0 ? Orthogonal
ma + kx = 0

41. Atom: Hydrogen Wave Function Type
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Measurements close to mean
Braking Radiation
Exponentially decreasing radial function

42. Solid: Resistivity of Metal
F = I L X B
?~T
J = ? Fdt
qvb = mv²/R

43. Ohm'S Law w/ current density
M? = 2dsin(?)
J = E s - s = Conductivity - E = Electric field
Exponentially decreasing radial function
I = V/R exp(-t/RC)

44. Mech: Centripetal Force
J/(ne) n: atom density
F = mv²/r
ds² = (c*dt)² - ?(x_i)²
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

45. Parallel axis theorem
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Dp/dt = L / (t ?V)
µ0 I1I2 / (2pd)
I = I_cm + (1/2)m d^2

46. SR: Total Energy of a Particle
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
P +1/2 ? v² + ?gh = Constant
I = -(c ?t)^2 + d^2
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

47. Rocket Equation
? = 1.22? / d
ds² = (c*dt)² - ?(x_i)²
NC?T
Dv = -udm/m - v = v0 + u ln(m0/m)

48. Thermo: 1st Law
Exp(N(µ-e)/t)
dQ = dW +dU
PdV +dU
C_eq = (? 1/C_i)^-1

49. Thermo: Monatomic gas ?=?
? = 5/3
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
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
C_eq = (? 1/C_i)^-1

50. EM: AC Resonance
X_L = X_C or X_total = 0
Measurements close to mean
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
U - ts = -tlog(Z)