Test your basic knowledge |

GRE Physics

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. Resonance frequency of LC circuit
Dp/dt = L / (t ?V)
1/vLC
?? = h/mc * (1-cos(?))
U - ts = -tlog(Z)

2. Volumetric Expansion
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
V = V0 + V0 a ?T
C_eq = ?C_i
Q = CVexp(-t/RC)

3. EM: Maxwell'S equations
E = <?| 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)
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.
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

4. Rayleigh'S Criterion
Sin(?) = ?/d
(° of Freedom)kT/2
E = <?| H |?>
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

5. Coriolis Force
F = -2*m(? x r)
X_L = i?L
E = <?| H |?>
I_z = I_x + I_y (think hoop symmetry)

6. Thermo: Monatomic gas ?=?
? = 5/3
Opposing charge induced upon conductor
DW/dq
PdV +dU

7. Quant: [L_x -L_y] = ?
Infinitely close to equilibrium at all times
ih_barL_z
(° of Freedom)kT/2
P/A = s T^4

8. Helmholtz Free Energy
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.
U - ts = -tlog(Z)
C_eq = ?C_i
Hbar*?³/(p²c³exp(hbar?/t)-1)

9. Ohm'S Law w/ current density
Q = CVexp(-t/RC)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
F = µ0 q v I / 2pr
J = E s - s = Conductivity - E = Electric field

10. Lab: Precision of Measurements
F = mv²/r
Measurements close to mean
X_L = X_C or X_total = 0
Z_c = -i/(?C) ; Z_L = i ? L

11. Springs in series/parallel
E = s/e_0
Sin(?) = ?/d
Cos[?] Sin[?] -Sin[?] Cos[?]
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

12. Parallel axis theorem
I = I_cm + (1/2)m d^2
Measurements close to mean
Always Real
µ0 I1I2 / (2pd)

13. Force/length between two wires
µ0 I1I2 / (2pd)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
?s = 0 - ?l = ±1
.5 LI²

14. Single Slit Diffraction Maximum
H = H_0 + ?H
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
0
Asin(?) = m?

15. Thermo: Adiabatic Work vs Isothermal Work
W_A < W_I
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Q = CVexp(-t/RC)

16. First law of thermodynamics (explain direction of energy for each term)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
DW = P dV
C_eq = ?C_i

17. Quant: Expectation Value
<?|O|?>
? = 5/3
E = s/e_0
Z_c = -i/(?C) ; Z_L = i ? L

18. Atom: Bohr Theory Ionization
V(r) + L²2/2mr²
E = Z²*E1
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
I = Im (sinc²(a)) ; a = pai sin(?) / ?

19. Solid: Resistivity of Semi-Conductor
?~1/T
Faraday/Lenz: current inducted opposes the changing field
Cos[?] Sin[?] -Sin[?] Cos[?]
ds² = (c*dt)² - ?(x_i)²

20. Planck Radiation Law
N d flux / dt
M? = 2dsin(?)
I = I_cm + md²
Hbar*?³/(p²c³exp(hbar?/t)-1)

21. Rocket Equation
Hbar*?³/(p²c³exp(hbar?/t)-1)
Dv = -udm/m - v = v0 + u ln(m0/m)
I = Im (sinc²(a)) ; a = pai sin(?) / ?
F = R/2

22. Thermo: Partition Function
Z = ?g_i*exp(-E/kT)
?s = 0 - ?l = ±1
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.
L = T - V dL/dq = d/dt dL/dqdot

23. Internal Energy of an Ideal Gas
µ = Current * Area T = µ x B
(3/2) n R ?t
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Measurements close to mean

24. Solid: Resistivity of Metal
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
?~T
F = R/2
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

25. Stefan-Boltzmann law for blackbodies (power per area and T)
<T> = 1/2 * <dV/dx>
P/A = s T^4
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
µ = Current * Area T = µ x B

26. Astro: Kepler'S Third Law
P² ~ R³
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
qvb = mv²/R
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

27. Work in a capacitor
E²-p²c²
1/2 CV²
<T> = -<V>/2
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

28. 3 Laws of Thermo
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
<?|O|?>
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
F = I L X B

29. Thermo: Blackbody Radiation
(3/2) n R ?t
ma + kx = 0
E = <?| H |?>
F = s * T4

30. EM: AC Resonance
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
F = R/2
X_L = X_C or X_total = 0
Measurements close to mean

31. Energy in Inductor
.5 LI²
Cv = dE/dT = 3R
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
µ = m_e/2

32. Thermo: 1st Law
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Dv = -udm/m - v = v0 + u ln(m0/m)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
dQ = dW +dU

33. Lab: Accuracy of Measurements
I = I_cm + md²
(3/2) n R ?t
Measurements close to true value
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

34. Force exerted on charge by long wire
F = µ0 q v I / 2pr
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
N d flux / dt

35. Boltzmann / Canonical distribution
ma + kx = 0
Dv = -udm/m - v = v0 + u ln(m0/m)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

36. Bernoulli Equation
L = mr²d?/dt
P +1/2 ? v² + ?gh = Constant
µ0 I1I2 / (2pd)
C_eq = ?C_i

37. EM: Method of Images
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Opposing charge induced upon conductor
N d flux / dt

38. Lensmaker Equation - Thin Lens
Asin(?) = m?
I = I_cm + (1/2)m d^2
ma + kx = 0
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

39. SR: Spacetime Interval
ds² = (c*dt)² - ?(x_i)²
4H + 2e- ? He +2? + 6?
? = ?0 root((1-v/c)/(1+v/c))
V(r) + L²2/2mr²

40. Wein'S Displacement Law
Z²/n² (m_red/m_elec)
µ0 I / 2R
? = h/mv
?max = 2.898 x 10 -³ / T

41. Focal point of mirrror with curvature
µ = Current * Area T = µ x B
E = s/e_0
F = R/2
?mv

42. Invariant Energy Quantity
(3/2) n R ?t
E²-p²c²
1/2 CV²
Isentropic

43. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
C = 4pe0 ab/(a-b) = inner and outer radii
E = <?| H |?>
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

44. Selection rules for atomic transitions
? = h/mv
1/vLC
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
1/2 CV²

45. Current in resistor in RC circuit
Dv = -udm/m - v = v0 + u ln(m0/m)
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.
E = <?| H |?>
I = V/R exp(-t/RC)

46. Magnetic Dipole Moment and Torque
F = R/2
?? = h/mc * (1-cos(?))
<?|O|?>
µ = Current * Area T = µ x B

47. Radiation (Larmor - and another neat fact)
4H + 2e- ? He +2? + 6?
Const: 2t = (n +.5)? Destructive 2t = n?
?max = 2.898 x 10 -³ / T
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

48. QM: de Broglie Wavelength
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
?= h/v(2mE)
U = t^2 d/dt (logZ)
Opposing charge induced upon conductor

49. Invariant spatial quantity
L = T - V dL/dq = d/dt dL/dqdot
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Ct²-x²-y²-z²
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

50. De Broglie wavelength
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
I = I_cm + md²
1/vLC
? = h/p