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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. Current in resistor in RC circuit
.5 CV²
DS = 0 - dQ = 0 - P V^? = constant
F_f = µ*F_N
I = V/R exp(-t/RC)

2. Force/length between two wires
Infinitely close to equilibrium at all times
µ0 I1I2 / (2pd)
?_max = b/T
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

3. Hamiltonian and Hamilton'S equations
? exp(-e/t)
? = h/mv
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
KE = 1/2 * µ (dr/dt)² L = µ r x v

4. Expectation value of the energy of state |?>
E = <?| H |?>
(3/2) n R ?t
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
v(mean)

5. Mech: Force of Friction
F_f = µ*F_N
E = s/e_0
? = ?0 root((1-v/c)/(1+v/c))
?_max = b/T

6. Force on a wire in magnetic field
F = I L X B
Hbar*?³/(p²c³exp(hbar?/t)-1)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

7. Rocket Equation
4H + 2e- ? He +2? + 6?
F = -2*m(? x r)
?mc²
Dv = -udm/m - v = v0 + u ln(m0/m)

8. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
E = s/e_0
DS = 0 - dQ = 0 - P V^? = constant
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

9. Work done on a gas
µ = m_e/2
(° of Freedom)kT/2
dU = 0 ? dS = ?dW/T
DW = P dV

10. Quant: Expectation Value
Asin(?) = m?
<?|O|?>
V(r) + L²2/2mr²
X_C = 1/(i?C)

11. Atom: Bohr Theory Ionization
? = 1.22? / d
E = Z²*E1
?_max = b/T
?mc²

12. Single Slit Diffraction Intensity
I = Im (sinc²(a)) ; a = pai sin(?) / ?
? (t-vx/c²)
I = I_cm + md²
Exponentially decreasing radial function

13. Induced EMF of solenoid
N d flux / dt
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
DS = 0 - dQ = 0 - P V^? = constant
F = f* (c+v_r)/(c+v_s)

14. Astro: Aperture Formula (Rayleigh Criterion)
F = s * T4
?s = 0 - ?l = ±1
? = 1.22?/D
Ct²-x²-y²-z²

15. EM: Series Capacitance
C_eq = (? 1/C_i)^-1
? = h/mv
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
KE = 1/2 * µ (dr/dt)² L = µ r x v

16. EM: Lorentz Force
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
F = qv×B
?_max = b/T
N d flux / dt

17. De Broigle Wavelength
Z = ?g_i*exp(-E/kT)
E = <?| H |?>
? = h/mv
P +1/2 ? v² + ?gh = Constant

18. Thermo: Blackbody Radiation
DW = P dV
Always Real
F = s * T4
U - ts = -tlog(Z)

19. Bar magnets -- direction of B field lines - earth'S B field
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
?~1/T
? (t-vx/c²)
M? = 2dsin(?)

20. Polarizers - intensity when crossed at ?
(° of Freedom)kT/2
1/2 CV²
X_C = 1/(i?C)
I = I_0 Cos[?]^2

21. EM: Maxwell'S equations
.5 CV²
A[B -C] + [A -C]B
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
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. Selection rules for atomic transitions
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
X_C = 1/(i?C)
P² ~ R³

23. Work (P - V)
P1V1 - P2V2 / (? - 1)
I = I_cm + (1/2)m d^2
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
?_max = b/T

24. E field of a capacitor (d->0)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
P² ~ R³
E = s/e_0
?s = 0 - ?l = ±1

25. Magnetic Field of a long solenoid
I = -(c ?t)^2 + d^2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
B = µ0 I n
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

26. EM: AC Resonance
U = t^2 d/dt (logZ)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
? (t-vx/c²)
X_L = X_C or X_total = 0

27. Self Inductance
(3/2) n R ?t
V = -L di/dt
Exponentially decreasing radial function
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.

28. A reversible process stays..
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Infinitely close to equilibrium at all times
dQ = dW +dU
?mv

29. 3 Laws of Thermo
P1V1 - P2V2 / (? - 1)
?mv
µ0 I1I2 / (2pd)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

30. Bohr Model: Energy
Z²/n² (m_red/m_elec)
µ=s^2
V(r) + L²2/2mr²
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. EM: Electric Field inside of Conductor
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
?mv
ma + kx = 0
0

32. Mech: Parallel Axis Theorem (Moment of Inertia)
Z_c = -i/(?C) ; Z_L = i ? L
I = I_cm + md²
Faraday/Lenz: current inducted opposes the changing field
µ0 I / 2R

33. Perturbations
H = H_0 + ?H
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
P² ~ R³
Dv = -udm/m - v = v0 + u ln(m0/m)

34. Bohr Model: Radii
N²/Z (m_elec/m_red)
<?1|?2> = 0 ? Orthogonal
F_f = µ*F_N
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

35. Mech: Virial Theorem
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
<T> = -<V>/2
NC?T
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

36. Thermo: Isothermal
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Exp(N(µ-e)/t)
dU = 0 ? dS = ?dW/T
L = mr²d?/dt

37. Mech: Rotational Energy
V = V0 + V0 a ?T
T = I?²/2
µ = Current * Area T = µ x B
X_L = X_C or X_total = 0

38. Relativistic Momentum
?mv
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
.5 CV²
Exponentially decreasing radial function

39. Coriolis Force
B = µ0 I n
F = -2*m(? x r)
F = I L X B
4H + 2e- ? He +2? + 6?

40. Relativistic Energy
Faraday/Lenz: current inducted opposes the changing field
Isentropic
?mc²
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

41. Doppler Shift for light
? = ?0 root((1-v/c)/(1+v/c))
? = h/mv
dQ = dW +dU
C = 4pe0 ab/(a-b) = inner and outer radii

42. td(entropy) =
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
PdV +dU
Always Real
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

43. De Broglie wavelength
(° of Freedom)kT/2
? = h/p
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
ma + kx = 0

44. Atom: Hydrogen Wave Function Type
Exponentially decreasing radial function
P +1/2 ? v² + ?gh = Constant
J = E s - s = Conductivity - E = Electric field
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

45. Addition of relativistic velocities

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46. Adiabatic means
P +1/2 ? v² + ?gh = Constant
I = I_cm + md²
Isentropic
P/A = s T^4

47. Quant: [L_x -L_y] = ?
Measurements close to mean
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Ct²-x²-y²-z²
ih_barL_z

48. Commutator identities ( [B -A C] - [A -B] )
V(r) + L²2/2mr²
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
V = -L di/dt
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

49. Entropy (# of states - and in terms of other thermo quantities)
? = 1.22?/D
I = Im (sinc²(a)) ; a = pai sin(?) / ?
S = k ln[O] ; dS = dQ/T
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

50. Thin Film Theory: Constructive / Destructive Interference
Const: 2t = (n +.5)? Destructive 2t = n?
?= h/v(2mE)
I = Im (sinc²(a)) ; a = pai sin(?) / ?
DS = 0 - dQ = 0 - P V^? = constant