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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. Partition Function
S_mean = s/Sqrt[N]
?= h/v(2mE)
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.
? exp(-e/t)

2. Radiation (Larmor - and another neat fact)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
? = ?0 root((1-v/c)/(1+v/c))
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Sin(?) = ?/d

3. Volumetric Expansion
u dm/dt
V = V0 + V0 a ?T
Dv = -udm/m - v = v0 + u ln(m0/m)
Isentropic

4. Single Slit Diffraction Maximum
Asin(?) = m?
? (t-vx/c²)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

5. Wein'S Displacement Law
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
?max = 2.898 x 10 -³ / T
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
E = Z²*E1

6. Triplet/singlet states: symmetry and net spin
.5 CV²
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
F_f = µ*F_N
P1V1 - P2V2 / (? - 1)

7. Charge in Capacitor
P1V1 - P2V2 / (? - 1)
X_L = i?L
Q = CVexp(-t/RC)
PdV +dU

8. EM: Reactance of Inductor
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.
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
X_L = i?L
1/ne - where n is charge carrier density

9. Gibbs Factor
dU = 0 ? dS = ?dW/T
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Exp(N(µ-e)/t)
J/(ne) n: atom density

10. 3 Laws of Thermo
L = mr²d?/dt
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Z²/n² (m_red/m_elec)
I_z = I_x + I_y (think hoop symmetry)

11. Force on a wire in magnetic field
F = mv²/r
F = I L X B
KE = 1/2 * µ (dr/dt)² L = µ r x v
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

12. Malus Law

13. Resistance - length - area - rho
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
U - ts = -tlog(Z)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

14. Mech: Force of Friction
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
ih_barL_z
F_f = µ*F_N

15. Wein'S displacement law for blackbodies (? and T)
?_max = b/T
? = 1.22? / d
v(mean)
I = Im (sinc²(a)) ; a = pai sin(?) / ?

16. Atom: Bohr Formula
Q = CVexp(-t/RC)
Cv = dE/dT = 3R
KE = 1/2 * µ (dr/dt)² L = µ r x v
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

17. Helmholtz Free Energy
U - ts = -tlog(Z)
Cv = dE/dT = 3R
?= h/v(2mE)
Ct²-x²-y²-z²

18. EM: Bremsstrahlung (translation)
Isentropic
F = R/2
Braking Radiation
DW/dq

19. First law of thermodynamics (explain direction of energy for each term)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
ma + kx = 0
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
F = -2*m(? x r)

20. SR: Spacetime Interval
F = µ0 q v I / 2pr
<?1|?2> = 0 ? Orthogonal
ds² = (c*dt)² - ?(x_i)²
L = T - V dL/dq = d/dt dL/dqdot

21. Focal point of mirrror with curvature
1/ne - where n is charge carrier density
dQ = dW +dU
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
F = R/2

22. 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.
Sin(?) = ?/d
B = µ0 I n
J = E s - s = Conductivity - E = Electric field

23. Magnetic Dipole Moment and Torque
Measurements close to true value
V = V0 + V0 a ?T
µ = Current * Area T = µ x B
F = -2*m(? x r)

24. Mech: Virial Theorem
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(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
<T> = -<V>/2
U - ts = -tlog(Z)

25. Dulong Petit Law
J = ? Fdt
F = qv×B
C_eq = (? 1/C_i)^-1
Cv = dE/dT = 3R

26. Bohr Model: Energy
Q = CVexp(-t/RC)
?s = 0 - ?l = ±1
Z²/n² (m_red/m_elec)
Exp(N(µ-e)/t)

27. Relativistic Energy
I = I_0 Cos[?]^2
?mc²
<?|O|?>
? exp(-e/t)

28. Double Slit: Interference Minimum - Diffraction Minimum
F_f = µ*F_N
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

29. Bragg'S Law of Reflection
M? = 2dsin(?)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
F_f = µ*F_N
(3/2) n R ?t

30. How to derive cylcotron frequency
Opposing charge induced upon conductor
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
qvb = mv²/R
.5 CV²

31. Lagrangian and Lagrange'S equation
Asin(?) = m?
L = T - V dL/dq = d/dt dL/dqdot
W_A < W_I
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

32. EM: Maxwell'S equations
E = Z²*E1
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
T^2 = k R^3 - k=constant
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

33. Clausius-Clapeyron Equation
Dp/dt = L / (t ?V)
? = 5/3
?~1/T
U - ts = -tlog(Z)

34. Hall Coefficient
1/ne - where n is charge carrier density
µ0 I / 2R
dU = 0 ? dS = ?dW/T
Dp/dt = L / (t ?V)

35. Pauli matrices
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
? = 1.22?/D
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Infinitely close to equilibrium at all times

36. EM: Lorentz Force
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
V = V0 + V0 a ?T
P/A = s T^4
F = qv×B

37. Relativistic length contraction
L = L_0 Sqrt[1-v^2/c^2]
Asin(?) = m?
µ=s^2
Measurements close to mean

38. Mech: Impulse
0
J = ? Fdt
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
?s = 0 - ?l = ±1

39. Adiabatic processes (dS - dQ - P and V)
? = 5/3
DS = 0 - dQ = 0 - P V^? = constant
P +1/2 ? v² + ?gh = Constant
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.

40. EM: Method of Images
DS = 0 - dQ = 0 - P V^? = constant
N d flux / dt
Opposing charge induced upon conductor
U - ts = -tlog(Z)

41. EM: Parallel Capacitance
1/vLC
C_eq = ?C_i
P +1/2 ? v² + ?gh = Constant
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.

42. Thermo: Isothermal
dU = 0 ? dS = ?dW/T
.5 LI²
PdV +dU
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

43. EM: Electromagnetic inertia
Faraday/Lenz: current inducted opposes the changing field
T = I?²/2
Opposing charge induced upon conductor
I_z = I_x + I_y (think hoop symmetry)

44. Commutator identities ( [B -A C] - [A -B] )
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
?~T
?s = 0 - ?l = ±1

45. Force exerted on charge by long wire
F = µ0 q v I / 2pr
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Z_c = -i/(?C) ; Z_L = i ? L
E = s/e_0

46. Polarizers - intensity when crossed at ?
Cos[?] Sin[?] -Sin[?] Cos[?]
I = I_0 Cos[?]^2
?max = 2.898 x 10 -³ / T
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

47. Quant: [L_x -L_y] = ?
ih_barL_z
<?|O|?>
P +1/2 ? v² + ?gh = Constant
µ=s^2

48. Atom: Orbital Config
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
µ0 I1I2 / (2pd)
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
Dv = -udm/m - v = v0 + u ln(m0/m)

49. Entropy (# of states - and in terms of other thermo quantities)
<?|O|?>
dQ = dW +dU
T = I?²/2
S = k ln[O] ; dS = dQ/T

50. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
S = k ln[O] ; dS = dQ/T
µ = m_e/2