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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)
µ0 I1I2 / (2pd)
P/A = s T^4
? = 1.22?/D
?mc²

2. Gibbs Factor
F = -2*m(? x r)
Exp(N(µ-e)/t)
F = s * T4
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

3. Angular momentum - Central Force Motion
? (t-vx/c²)
L = mr²d?/dt
Int ( A . dr) = Int ( del x A) dSurface
Z = ?g_i*exp(-E/kT)

4. Mech: Centripetal Force
µ0 I / 2R
? = 5/3
F = mv²/r
? = ?0 root((1-v/c)/(1+v/c))

5. Thermo: Monatomic gas ?=?
?mc²
? = 5/3
<T> = -<V>/2
PdV +dU

6. EM: Parallel Capacitance
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
C_eq = ?C_i
u dm/dt
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

7. Mech: Impulse
T = I?²/2
J = ? Fdt
0
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.

8. EM: Electric Field inside of Conductor
0
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
?s = 0 - ?l = ±1
T^2 = k R^3 - k=constant

9. Springs in series/parallel
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
F = s * T4
DW/dq
µ0 I1I2 / (2pd)

10. Energy levels from the Coulomb potential
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
(° of Freedom)kT/2
P1V1 - P2V2 / (? - 1)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

11. Doppler shift for light
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
N d flux / dt
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

12. Kepler'S Three Laws
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
dQ = dW +dU
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
E = <?| H |?>

13. Relativistic Momentum
µ0 I / 2pR
?mv
?? = h/mc * (1-cos(?))
J = E s - s = Conductivity - E = Electric field

14. Invariant Energy Quantity
1/2 CV²
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
E²-p²c²

15. Selection Rules
ih_barL_z
?mc²
P² ~ R³
?s = 0 - ?l = ±1

16. EM: Maxwell'S equations
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
I = V/R exp(-t/RC)
I = Im (sinc²(a)) ; a = pai sin(?) / ?
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

17. Self Inductance
?mv
V = -L di/dt
KE = 1/2 * µ (dr/dt)² L = µ r x v
E²-p²c²

18. Atom: Bohr Theory Ionization
? = ?0 root((1-v/c)/(1+v/c))
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
H = H_0 + ?H
E = Z²*E1

19. Ohm'S Law w/ current density
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
X_L = X_C or X_total = 0
Faraday/Lenz: current inducted opposes the changing field
J = E s - s = Conductivity - E = Electric field

20. Atom: Hydrogen Wave Function Type
(3/2) n R ?t
Exponentially decreasing radial function
F_f = µ*F_N
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.

21. EM: Method of Images
? = 1.22?/D
?~1/T
Opposing charge induced upon conductor
Faraday/Lenz: current inducted opposes the changing field

22. Kepler'S third law (T and R)
E = Z²*E1
B = µ0 I n
F = I L X B
T^2 = k R^3 - k=constant

23. Dulong Petit Law
F = µ0 q v I / 2pr
µ0 I / 2R
Opposing charge induced upon conductor
Cv = dE/dT = 3R

24. Relativistic Energy
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
I = Im (sinc²(a)) ; a = pai sin(?) / ?
(3/2) n R ?t
?mc²

25. EM: AC Resonance
Dv = -udm/m - v = v0 + u ln(m0/m)
?~1/T
X_L = X_C or X_total = 0
B = µ0 I n

26. QM: de Broglie Wavelength
?= h/v(2mE)
L = mr²d?/dt
µ = m_e/2
U = t^2 d/dt (logZ)

27. EM: Electromagnetic inertia
Faraday/Lenz: current inducted opposes the changing field
? = 1.22? / d
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
.5 CV²

28. Lab: Precision of Measurements
Measurements close to mean
L = L_0 Sqrt[1-v^2/c^2]
T^2 = k R^3 - k=constant
I ' = I cos²(?)

29. Force on a wire in magnetic field
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
F = I L X B
?s = 0 - ?l = ±1
Sin(?) = ?/d

30. De Broglie wavelength
? = h/p
S = k ln[O] ; dS = dQ/T
<?1|?2> = 0 ? Orthogonal
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

31. Mean electron drift speed
NC?T
ds² = (c*dt)² - ?(x_i)²
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.
J/(ne) n: atom density

32. How to derive cylcotron frequency
qvb = mv²/R
Z²/n² (m_red/m_elec)
Cos[?] Sin[?] -Sin[?] Cos[?]
F = I L X B

33. Electromotive Force
DW/dq
dU = 0 ? dS = ?dW/T
(3/2) n R ?t
X_L = i?L

34. Adiabatic means
.5 LI²
1/ne - where n is charge carrier density
DW = P dV
Isentropic

35. Effective Potential
J = E s - s = Conductivity - E = Electric field
µ0 I / 2R
J/(ne) n: atom density
V(r) + L²2/2mr²

36. td(entropy) =
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
PdV +dU
?_max = b/T
F = I L X B

37. Stark Effect
V = -L di/dt
NC?T
Z = ?g_i*exp(-E/kT)
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

38. Rayleigh'S Criterion
? exp(-e/t)
E = s/e_0
0
Sin(?) = ?/d

39. Mech: Virial Theorem
A[B -C] + [A -C]B
?~1/T
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
<T> = -<V>/2

40. Work done on a gas
DW = P dV
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
NC?T
Braking Radiation

41. Center of Mass: Kinetic Energy & Angular Momentum
ih_barL_z
Opposing charge induced upon conductor
KE = 1/2 * µ (dr/dt)² L = µ r x v
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

42. Bar magnets -- direction of B field lines - earth'S B field
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
F = µ0 q v I / 2pr
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Isentropic

43. Resonance frequency of LC circuit
Measurements close to mean
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
1/vLC
µ0 I1I2 / (2pd)

44. Atom: Orbital Config
T = I?²/2
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
<T> = -<V>/2
?mc²

45. Quant: Eigenvalue of Hermitian Operator
Always Real
I = V/R exp(-t/RC)
T = I?²/2
PdV +dU

46. Weighted average (mean and unc. of mean)
E = <?| H |?>
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

47. Complex impedance (expressions for capacitor and inductor)
Cos[?] Sin[?] -Sin[?] Cos[?]
Z_c = -i/(?C) ; Z_L = i ? L
(° of Freedom)kT/2
<?1|?2> = 0 ? Orthogonal

48. Magnetic Dipole Moment and Torque
.5 LI²
W_A < W_I
µ = Current * Area T = µ x B
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

49. Heat added
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
NC?T
C = 4pe0 ab/(a-b) = inner and outer radii

50. Work (P - V)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
P1V1 - P2V2 / (? - 1)
?mv
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2