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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. Magnetic Dipole Moment and Torque
?= h/v(2mE)
J = E s - s = Conductivity - E = Electric field
µ = Current * Area T = µ x B
M? = 2dsin(?)

2. First law of thermodynamics (explain direction of energy for each term)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
P +1/2 ? v² + ?gh = Constant
.5 LI²
µ0 I / 2R

3. Angular momentum operators L^2 and L_z
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
(3/2) n R ?t
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
dU = 0 ? dS = ?dW/T

4. Energy levels from the Coulomb potential
.5 LI²
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
?? = h/mc * (1-cos(?))
dU = 0 ? dS = ?dW/T

5. Thermo: Isothermal
dU = 0 ? dS = ?dW/T
<?1|?2> = 0 ? Orthogonal
Opposing charge induced upon conductor
KE = 1/2 * µ (dr/dt)² L = µ r x v

6. Ohm'S Law w/ current density
E = <?| H |?>
V = -L di/dt
.5 LI²
J = E s - s = Conductivity - E = Electric field

7. Complex impedance (expressions for capacitor and inductor)
Z = ?g_i*exp(-E/kT)
Z_c = -i/(?C) ; Z_L = i ? L
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
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

8. Kepler'S third law (T and R)
PdV +dU
Asin(?) = m?
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
T^2 = k R^3 - k=constant

9. Boltzmann / Canonical distribution
Ct²-x²-y²-z²
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
L = T - V dL/dq = d/dt dL/dqdot
Q = CVexp(-t/RC)

10. Helmholtz Free Energy
µ0 I1I2 / (2pd)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
U - ts = -tlog(Z)

11. Source-free RC Circuit
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
I = I_cm + md²
?max = 2.898 x 10 -³ / T
µ = Current * Area T = µ x B

12. Commutator identities ( [B -A C] - [A -B] )
P +1/2 ? v² + ?gh = Constant
C_eq = ?C_i
F = f* (c+v_r)/(c+v_s)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

13. Quant: Eigenvalue of Hermitian Operator
I = I_cm + md²
PdV +dU
Always Real
N d flux / dt

14. Current in resistor in RC circuit
1/vLC
T = I?²/2
?mv
I = V/R exp(-t/RC)

15. EM: Reactance of Inductor
4H + 2e- ? He +2? + 6?
U = t^2 d/dt (logZ)
I = -(c ?t)^2 + d^2
X_L = i?L

16. Wein'S displacement law for blackbodies (? and T)
?_max = b/T
µ=s^2
F = s * T4
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

17. Springs in series/parallel
Int ( A . dr) = Int ( del x A) dSurface
µ0 I / 2pR
C = 4pe0 ab/(a-b) = inner and outer radii
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

18. Doppler Shift in Frequency
DW/dq
dQ = dW +dU
F = f* (c+v_r)/(c+v_s)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

19. Energy in Inductor
ds² = (c*dt)² - ?(x_i)²
Measurements close to true value
I = Im (sinc²(a)) ; a = pai sin(?) / ?
.5 LI²

20. Selection Rules
µ0 I / 2R
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
?s = 0 - ?l = ±1
F = s * T4

21. EM: Maxwell'S equations
u dm/dt
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Const: 2t = (n +.5)? Destructive 2t = n?
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

22. Energy in a Capacitor
I = Im (sinc²(a)) ; a = pai sin(?) / ?
F = qv×B
E = Z²*E1
.5 CV²

23. Doppler shift for light
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.
P1V1 - P2V2 / (? - 1)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
<T> = -<V>/2

24. Lagrangian and Lagrange'S equation
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
L = T - V dL/dq = d/dt dL/dqdot
ds² = (c*dt)² - ?(x_i)²
V = -L di/dt

25. De Broglie wavelength
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
PdV +dU
? = ?0 root((1-v/c)/(1+v/c))
? = h/p

26. Work (P - V)
J/(ne) n: atom density
J = ? Fdt
Braking Radiation
P1V1 - P2V2 / (? - 1)

27. Spherical Capacitor Equation
C = 4pe0 ab/(a-b) = inner and outer radii
L = T - V dL/dq = d/dt dL/dqdot
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
?mv

28. Biot-Savart law
<?1|?2> = 0 ? Orthogonal
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
E²-p²c²

29. td(entropy) =
L = L_0 Sqrt[1-v^2/c^2]
PdV +dU
? = 5/3
qvb = mv²/R

30. Bar magnets -- direction of B field lines - earth'S B field
S = k ln[O] ; dS = dQ/T
L = L_0 Sqrt[1-v^2/c^2]
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
?_max = b/T

31. EM: Electromagnetic inertia
X_L = X_C or X_total = 0
Faraday/Lenz: current inducted opposes the changing field
(° of Freedom)kT/2
ma + kx = 0

32. EM: Bremsstrahlung (translation)
M? = 2dsin(?)
Braking Radiation
Hbar*?³/(p²c³exp(hbar?/t)-1)
I = Im (sinc²(a)) ; a = pai sin(?) / ?

33. Perpendicular axis theorem
I_z = I_x + I_y (think hoop symmetry)
1/2 CV²
E = s/e_0
N d flux / dt

34. QM: de Broglie Wavelength
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
?= h/v(2mE)
E²-p²c²
? exp(-e/t)

35. Bohr Model: Radii
N²/Z (m_elec/m_red)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

36. Adiabatic means
Z_c = -i/(?C) ; Z_L = i ? L
PdV +dU
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Isentropic

37. Lab: Accuracy of Measurements
Measurements close to true value
? = 1.22?/D
F = R/2
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

38. Clausius-Clapeyron Equation
F_f = µ*F_N
I = I_cm + md²
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.
Dp/dt = L / (t ?V)

39. Resonance frequency of LC circuit
v(mean)
1/vLC
Cv = dE/dT = 3R
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

40. Inductance of Solenoid
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
A[B -C] + [A -C]B
N²/Z (m_elec/m_red)

41. Anomalous Zeeman Effect

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42. Dulong Petit Law
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
L = L_0 Sqrt[1-v^2/c^2]
Opposing charge induced upon conductor
Cv = dE/dT = 3R

43. Astro: Kepler'S Third Law
?= h/v(2mE)
Exponentially decreasing radial function
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
P² ~ R³

44. RLC resonance condition
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
dU = 0 ? dS = ?dW/T
Measurements close to mean
? = 1.22? / d

45. Atom: Orbital Config
I = I_cm + md²
P +1/2 ? v² + ?gh = Constant
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

46. Poisson distribution (µ and s)
µ=s^2
E = <?| H |?>
T^2 = k R^3 - k=constant
V(r) + L²2/2mr²

47. Kepler'S Three Laws
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
I = I_cm + (1/2)m d^2
?s = 0 - ?l = ±1
dQ = dW +dU

48. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
4H + 2e- ? He +2? + 6?
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
F = s * T4
I = -(c ?t)^2 + d^2

49. Triplet/singlet states: symmetry and net spin
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
? = h/mv
I = -(c ?t)^2 + d^2

50. Magnetic field due to a segment of wire
I = I_cm + md²
?? = h/mc * (1-cos(?))
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
U = t^2 d/dt (logZ)