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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. A reversible process stays..
dQ = dW +dU
Infinitely close to equilibrium at all times
qvb = mv²/R
.5 LI²

2. Double Slit: Interference Minimum - Diffraction Minimum
µ = m_e/2
Ct²-x²-y²-z²
Q = CVexp(-t/RC)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

3. Mech: Force of Friction
F_f = µ*F_N
F = I L X B
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Z_c = -i/(?C) ; Z_L = i ? L

4. Astro: Kepler'S Third Law
P² ~ R³
Measurements close to true value
F = R/2
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

5. Stark Effect
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
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
PdV +dU

6. Solid: Resistivity of Metal
P² ~ R³
S_mean = s/Sqrt[N]
Q = CVexp(-t/RC)
?~T

7. Hall Coefficient
? (t-vx/c²)
1/ne - where n is charge carrier density
Isentropic
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

8. EM: Bremsstrahlung (translation)
Braking Radiation
.5 LI²
Isentropic
0

9. RLC resonance condition
Faraday/Lenz: current inducted opposes the changing field
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
X_C = 1/(i?C)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

10. Bar magnets -- direction of B field lines - earth'S B field
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Braking Radiation
µ = m_e/2
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

11. Work done on a gas
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
DW = P dV
dQ = dW +dU
? = h/mv

12. Rotation matrix (2x2)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
u dm/dt
Cos[?] Sin[?] -Sin[?] Cos[?]
DW/dq

13. Electromotive Force
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
DW/dq
Hbar*?³/(p²c³exp(hbar?/t)-1)

14. Lagrangian and Lagrange'S equation
C_eq = (? 1/C_i)^-1
L = T - V dL/dq = d/dt dL/dqdot
? = h/mv
V = -L di/dt

15. Hamiltonian and Hamilton'S equations
µ0 I1I2 / (2pd)
µ0 I / 2R
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Measurements close to true value

16. Angular momentum operators L^2 and L_z
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>
Q = CVexp(-t/RC)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

17. Ohm'S Law w/ current density
F = I L X B
NC?T
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
J = E s - s = Conductivity - E = Electric field

18. Coriolis Force
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
4H + 2e- ? He +2? + 6?
X_L = i?L
F = -2*m(? x r)

19. Doppler shift for light
Measurements close to mean
dU = 0 ? dS = ?dW/T
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

20. EM: Reactance of Capacitor
1/ne - where n is charge carrier density
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
µ = m_e/2
X_C = 1/(i?C)

21. Energy levels from the Coulomb potential
dU = 0 ? dS = ?dW/T
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
N²/Z (m_elec/m_red)

22. Wein'S Displacement Law
Measurements close to true value
?max = 2.898 x 10 -³ / T
Sin(?) = ?/d
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

23. Springs in series/parallel
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
<?1|?2> = 0 ? Orthogonal
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

24. Magnetic Field For Current in Long Wire
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
µ0 I / 2pR
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

25. Complex impedance (expressions for capacitor and inductor)
T^2 = k R^3 - k=constant
S_mean = s/Sqrt[N]
Z_c = -i/(?C) ; Z_L = i ? L
? exp(-e/t)

26. Polarizers - intensity when crossed at ?
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/vLC
I = I_0 Cos[?]^2
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

27. Virial Theorem
4H + 2e- ? He +2? + 6?
<T> = 1/2 * <dV/dx>
µ0 I1I2 / (2pd)
Hbar*?³/(p²c³exp(hbar?/t)-1)

28. Selection rules for atomic transitions
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
J/(ne) n: atom density
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
?? = h/mc * (1-cos(?))

29. Thermo: Partition Function
Z = ?g_i*exp(-E/kT)
Z_c = -i/(?C) ; Z_L = i ? L
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
dU = 0 ? dS = ?dW/T

30. Lab: Accuracy of Measurements
Dp/dt = L / (t ?V)
Int ( A . dr) = Int ( del x A) dSurface
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Measurements close to true value

31. Expectation value of the energy of state |?>
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
E = <?| 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
u dm/dt

32. Kepler'S Three Laws
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
H = H_0 + ?H
L = T - V dL/dq = d/dt dL/dqdot
u dm/dt

33. Quant: Commutator Relation [AB -C]
A[B -C] + [A -C]B
? = 1.22?/D
µ = m_e/2
P² ~ R³

34. Volumetric Expansion
Sin(?) = ?/d
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Exp(N(µ-e)/t)
V = V0 + V0 a ?T

35. Wein'S displacement law for blackbodies (? and T)
?_max = b/T
Ct²-x²-y²-z²
DW/dq
?mc²

36. Relativistic Momentum
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
F = f* (c+v_r)/(c+v_s)
? = 5/3

37. EM: Lorentz Force
? = 5/3
PdV +dU
J/(ne) n: atom density
F = qv×B

38. Triplet/singlet states: symmetry and net spin
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Z²/n² (m_red/m_elec)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
<T> = 1/2 * <dV/dx>

39. Poisson distribution (µ and s)
I = Im (sinc²(a)) ; a = pai sin(?) / ?
µ=s^2
ih_barL_z
(° of Freedom)kT/2

40. De Broglie wavelength
Int ( A . dr) = Int ( del x A) dSurface
? = h/p
E²-p²c²
Exponentially decreasing radial function

41. Law of Mass Action
I = Im (sinc²(a)) ; a = pai sin(?) / ?
U = t^2 d/dt (logZ)
?s = 0 - ?l = ±1
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

42. SR: Total Energy of a Particle
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

43. Source Free RL Circuit
X_C = 1/(i?C)
<?1|?2> = 0 ? Orthogonal
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
ma + kx = 0

44. EM: AC Resonance
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
DW/dq
X_L = X_C or X_total = 0
X_L = i?L

45. Rocket Equation
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Dv = -udm/m - v = v0 + u ln(m0/m)
F = R/2
µ0 I1I2 / (2pd)

46. Lensmaker Equation - Thin Lens
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
F = µ0 q v I / 2pr
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
M? = 2dsin(?)

47. De Broigle Wavelength
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Const: 2t = (n +.5)? Destructive 2t = n?
? = h/mv

48. Thermo: Average Total Energy
Q = CVexp(-t/RC)
<T> = 1/2 * <dV/dx>
S = k ln[O] ; dS = dQ/T
(° of Freedom)kT/2

49. Delta Function Potential - type of WF
DW = P dV
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
F_f = µ*F_N
ih_barL_z

50. Self Inductance
V = -L di/dt
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/T
X_L = i?L