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. Radiation (Larmor - and another neat fact)
X_L = i?L
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
X_C = 1/(i?C)

2. Thermo: Monatomic gas ?=?
Exp(N(µ-e)/t)
F = f* (c+v_r)/(c+v_s)
? = ?0 root((1-v/c)/(1+v/c))
? = 5/3

3. Doppler shift for light
KE = 1/2 * µ (dr/dt)² L = µ r x v
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

4. Magnetic Field Through Ring
µ0 I / 2R
P² ~ R³
dQ = dW +dU
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

5. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
V = V0 + V0 a ?T
U = t^2 d/dt (logZ)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

6. Volumetric Expansion
W_A < W_I
?~T
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
V = V0 + V0 a ?T

7. Poisson distribution (µ and s)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Hbar*?³/(p²c³exp(hbar?/t)-1)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
µ=s^2

8. Lagrangian and Lagrange'S equation
E = Z²*E1
V = -L di/dt
L = T - V dL/dq = d/dt dL/dqdot
1/2 CV²

9. Invariant spatial quantity
µ0 I / 2R
U = t^2 d/dt (logZ)
Int ( A . dr) = Int ( del x A) dSurface
Ct²-x²-y²-z²

10. Hall Coefficient
? = 5/3
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
1/ne - where n is charge carrier density
V = -L di/dt

11. Thermo: Average Total Energy
S = k ln[O] ; dS = dQ/T
KE = 1/2 * µ (dr/dt)² L = µ r x v
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
(° of Freedom)kT/2

12. Kepler'S Three Laws
.5 LI²
?max = 2.898 x 10 -³ / T
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
T = I?²/2

13. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
Q = CVexp(-t/RC)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
DW = P dV
1/ne - where n is charge carrier density

14. Partition Function
I = I_0 Cos[?]^2
? exp(-e/t)
Dv = -udm/m - v = v0 + u ln(m0/m)
F = s * T4

15. Ohm'S Law w/ current density
L = T - V dL/dq = d/dt dL/dqdot
Exponentially decreasing radial function
V(r) + L²2/2mr²
J = E s - s = Conductivity - E = Electric field

16. Adiabatic means
Faraday/Lenz: current inducted opposes the changing field
<?1|?2> = 0 ? Orthogonal
Isentropic
V(r) + L²2/2mr²

17. Quant: Eigenvalue of Hermitian Operator
Always Real
I_z = I_x + I_y (think hoop symmetry)
<?|O|?>
? exp(-e/t)

18. Mech: Rotational Energy
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
T = I?²/2
F = mv²/r
S = k ln[O] ; dS = dQ/T

19. Astro: p-p Chain
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
4H + 2e- ? He +2? + 6?
?mv
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

20. Angular momentum - Central Force Motion
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
?~T
L = mr²d?/dt
Z_c = -i/(?C) ; Z_L = i ? L

21. Atom: Bohr Formula
X_C = 1/(i?C)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
?s = 0 - ?l = ±1
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

22. Thermo: 1st Law
dQ = dW +dU
V(r) + L²2/2mr²
1/2 CV²
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

23. Atom: Hydrogen Wave Function Type
µ0 I / 2pR
J/(ne) n: atom density
F = mv²/r
Exponentially decreasing radial function

24. Relativistic Energy
Asin(?) = m?
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
?mc²
E²-p²c²

25. Mech: Centripetal Force
E = <?| H |?>
F = mv²/r
X_L = X_C or X_total = 0
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

26. Rotation matrix (2x2)
<?1|?2> = 0 ? Orthogonal
Cos[?] Sin[?] -Sin[?] Cos[?]
µ = m_e/2
ma + kx = 0

27. Quant: Orthogonality of States
I ' = I cos²(?)
<?1|?2> = 0 ? Orthogonal
KE = 1/2 * µ (dr/dt)² L = µ r x v
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

28. RLC resonance condition
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
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
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

29. Effective Potential
V(r) + L²2/2mr²
? = h/mv
<?1|?2> = 0 ? Orthogonal
?s = 0 - ?l = ±1

30. Coriolis Force
? (t-vx/c²)
F = -2*m(? x r)
C_eq = (? 1/C_i)^-1
µ = m_e/2

31. Lab: Accuracy of Measurements
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
I_z = I_x + I_y (think hoop symmetry)
Measurements close to true value
?mc²

32. Relativistic length contraction
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
L = L_0 Sqrt[1-v^2/c^2]
E = Z²*E1
?_max = b/T

33. Adiabatic processes (dS - dQ - P and V)
E = s/e_0
Exponentially decreasing radial function
DS = 0 - dQ = 0 - P V^? = constant
L = L_0 Sqrt[1-v^2/c^2]

34. Single Slit Diffraction Intensity
? = ?0 root((1-v/c)/(1+v/c))
P +1/2 ? v² + ?gh = Constant
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Dp/dt = L / (t ?V)

35. Current in resistor in RC circuit
<?1|?2> = 0 ? Orthogonal
I = V/R exp(-t/RC)
? exp(-e/t)
F = mv²/r

36. EM: Maxwell'S equations
u dm/dt
M? = 2dsin(?)
dQ = dW +dU
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

37. Perturbations
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
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
? = h/p
H = H_0 + ?H

38. Triplet/singlet states: symmetry and net spin
dQ = dW +dU
I ' = I cos²(?)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

39. Bohr Model: Energy
F = R/2
<?|O|?>
µ=s^2
Z²/n² (m_red/m_elec)

40. Work (P - V)
S_mean = s/Sqrt[N]
P1V1 - P2V2 / (? - 1)
DS = 0 - dQ = 0 - P V^? = constant
?mc²

41. Thin Film Theory: Constructive / Destructive Interference
E = <?| H |?>
Const: 2t = (n +.5)? Destructive 2t = n?
F = f* (c+v_r)/(c+v_s)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

42. Thermo: Isothermal
ds² = (c*dt)² - ?(x_i)²
dU = 0 ? dS = ?dW/T
E = s/e_0
I = V/R exp(-t/RC)

43. Magnetic field due to a segment of wire
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
E = <?| H |?>
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Q = CVexp(-t/RC)

44. Thermo: Adiabatic Work vs Isothermal Work
?s = 0 - ?l = ±1
W_A < W_I
ma + kx = 0
Exponentially decreasing radial function

45. Mean electron drift speed
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
DS = 0 - dQ = 0 - P V^? = constant
J/(ne) n: atom density
E = s/e_0

46. EM: Bremsstrahlung (translation)
1/ne - where n is charge carrier density
Braking Radiation
Dp/dt = L / (t ?V)
(3/2) n R ?t

47. Quant: Commutator Relation [AB -C]
A[B -C] + [A -C]B
<?1|?2> = 0 ? Orthogonal
Int ( A . dr) = Int ( del x A) dSurface
Asin(?) = m?

48. Boltzmann / Canonical distribution
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
DS = 0 - dQ = 0 - P V^? = constant
Hbar*?³/(p²c³exp(hbar?/t)-1)
Const: 2t = (n +.5)? Destructive 2t = n?

49. Charge in Capacitor
<T> = 1/2 * <dV/dx>
Q = CVexp(-t/RC)
T^2 = k R^3 - k=constant
? exp(-e/t)

50. Polarizers - intensity when crossed at ?
.5 CV²
ds² = (c*dt)² - ?(x_i)²
I = I_0 Cos[?]^2
?~T