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. Source-free RC Circuit
W_A < W_I
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
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)

2. Bohr Model: Energy
Z²/n² (m_red/m_elec)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
? = 1.22?/D
Ct²-x²-y²-z²

3. Complex impedance (expressions for capacitor and inductor)
Z_c = -i/(?C) ; Z_L = i ? L
T^2 = k R^3 - k=constant
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
I = I_cm + md²

4. Perpendicular axis theorem
F = mv²/r
I_z = I_x + I_y (think hoop symmetry)
P +1/2 ? v² + ?gh = Constant
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

5. Doppler Shift for light
C_eq = (? 1/C_i)^-1
? = ?0 root((1-v/c)/(1+v/c))
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
J = ? Fdt

6. De Broglie wavelength
E = Z²*E1
? = h/p
<T> = -<V>/2
F = -2*m(? x r)

7. Lensmaker Equation - Thin Lens
E = Z²*E1
Infinitely close to equilibrium at all times
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
µ0 I / 2R

8. First law of thermodynamics (explain direction of energy for each term)
F = qv×B
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
? = ?0 root((1-v/c)/(1+v/c))
qvb = mv²/R

9. Springs in series/parallel
? exp(-e/t)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
? = 5/3

10. Lab: Standard Deviation of Poisson
T = I?²/2
L = T - V dL/dq = d/dt dL/dqdot
ds² = (c*dt)² - ?(x_i)²
v(mean)

11. EM: Maxwell'S equations
ma + kx = 0
µ = m_e/2
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
J = E s - s = Conductivity - E = Electric field

12. Effective Potential
V(r) + L²2/2mr²
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
I = I_cm + (1/2)m d^2
Asin(?) = m?

13. Source Free RL Circuit
Opposing charge induced upon conductor
Cos[?] Sin[?] -Sin[?] Cos[?]
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

14. Work (P - V)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
P1V1 - P2V2 / (? - 1)
µ = m_e/2
PdV +dU

15. Triplet/singlet states: symmetry and net spin
S_mean = s/Sqrt[N]
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
F = qv×B

16. Law of Mass Action
E = Z²*E1
qvb = mv²/R
? = 1.22?/D
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

17. Polarizers - intensity when crossed at ?
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_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)
P² ~ R³
I = I_0 Cos[?]^2

18. Self Inductance
Exp(N(µ-e)/t)
u dm/dt
V = -L di/dt
? exp(-e/t)

19. Doppler Shift in Frequency
F = f* (c+v_r)/(c+v_s)
Const: 2t = (n +.5)? Destructive 2t = n?
F = -2*m(? x r)
Z_c = -i/(?C) ; Z_L = i ? L

20. Angular momentum operators L^2 and L_z
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
I = I_0 Cos[?]^2
dU = 0 ? dS = ?dW/T
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

21. Expectation value of the energy of state |?>
NC?T
E = <?| H |?>
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
? = h/p

22. Lab: Accuracy of Measurements
Measurements close to true value
? = 1.22?/D
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Dp/dt = L / (t ?V)

23. Resonance frequency of LC circuit
T^2 = k R^3 - k=constant
1/vLC
F_f = µ*F_N
qvb = mv²/R

24. 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
E = <?| H |?>
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.
X_L = i?L

25. Force on a wire in magnetic field
C_eq = (? 1/C_i)^-1
F = I L X B
S = k ln[O] ; dS = dQ/T
?= h/v(2mE)

26. Helmholtz Free Energy
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
U - ts = -tlog(Z)
W_A < W_I
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

27. Stefan-Boltzmann law for blackbodies (power per area and T)
L = mr²d?/dt
0
P/A = s T^4
? (t-vx/c²)

28. EM: AC Resonance
(3/2) n R ?t
A[B -C] + [A -C]B
µ=s^2
X_L = X_C or X_total = 0

29. Work done on a gas
DW = P dV
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
F = mv²/r
M? = 2dsin(?)

30. EM: Series Capacitance
C_eq = (? 1/C_i)^-1
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
V(r) + L²2/2mr²
? = ?0 root((1-v/c)/(1+v/c))

31. EM: Electromagnetic inertia
F = qv×B
<?|O|?>
Faraday/Lenz: current inducted opposes the changing field
T = I?²/2

32. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
NC?T
L = T - V dL/dq = d/dt dL/dqdot
I = V/R exp(-t/RC)

33. Invariant Energy Quantity
µ0 I / 2R
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
E²-p²c²

34. Magnetic Dipole Moment and Torque
Z = ?g_i*exp(-E/kT)
µ = Current * Area T = µ x B
F = f* (c+v_r)/(c+v_s)
T = I?²/2

35. Commutator identities ( [B -A C] - [A -B] )
S_mean = s/Sqrt[N]
?_max = b/T
F = f* (c+v_r)/(c+v_s)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

36. Quant: Expectation Value
Braking Radiation
Sin(?) = ?/d
V = -L di/dt
<?|O|?>

37. Atom: Positronium Reduced Mass
µ = m_e/2
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Z²/n² (m_red/m_elec)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

38. Energy in Inductor
?~T
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
.5 LI²
E = Z²*E1

39. SR: Spacetime Interval
F = -2*m(? x r)
F = mv²/r
ds² = (c*dt)² - ?(x_i)²
v(mean)

40. Planck Radiation Law
F_f = µ*F_N
F = -2*m(? x r)
µ=s^2
Hbar*?³/(p²c³exp(hbar?/t)-1)

41. Thermo: Adiabatic Work vs Isothermal Work
(° of Freedom)kT/2
Asin(?) = m?
W_A < W_I
?= h/v(2mE)

42. Solid: Resistivity of Semi-Conductor
?~1/T
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
?_max = b/T
Exponentially decreasing radial function

43. Thermo: Average Total Energy
0
.5 LI²
(° of Freedom)kT/2
F = µ0 q v I / 2pr

44. Magnetic Field For Current in Long Wire
µ0 I / 2pR
L = L_0 Sqrt[1-v^2/c^2]
PdV +dU
Hbar*?³/(p²c³exp(hbar?/t)-1)

45. Delta Function Potential - type of WF
?_max = b/T
F = qv×B
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Asin(?) = m?

46. Perturbations
I = Im (sinc²(a)) ; a = pai sin(?) / ?
H = H_0 + ?H
Opposing charge induced upon conductor
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

47. Mech: Impulse
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
1/2 CV²
Braking Radiation
J = ? Fdt

48. Relativistic Energy
?mc²
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
I ' = I cos²(?)

49. Kepler'S Three Laws
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
X_L = i?L
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

50. Doppler shift for light
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
PdV +dU
(3/2) n R ?t