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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
J = E s - s = Conductivity - E = Electric field
X_L = X_C or X_total = 0
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. Solid: Resistivity of Metal
ma + kx = 0
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
S = k ln[O] ; dS = dQ/T

3. Work in a capacitor
?max = 2.898 x 10 -³ / T
u dm/dt
1/2 CV²
(° of Freedom)kT/2

4. Atom: Orbital Config
N d flux / dt
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Asin(?) = m?
(3/2) n R ?t

5. Force on a wire in magnetic field
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
C_eq = (? 1/C_i)^-1
F = I L X B
V = V0 + V0 a ?T

6. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
I = V/R exp(-t/RC)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Q = CVexp(-t/RC)

7. Rayleigh criterion
? = 1.22? / d
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
?max = 2.898 x 10 -³ / T
Exp(N(µ-e)/t)

8. Expectation value of the energy of state |?>
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Hbar*?³/(p²c³exp(hbar?/t)-1)
E = <?| H |?>

9. Thermo: 1st Law
U - ts = -tlog(Z)
I = I_cm + md²
dQ = dW +dU
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

10. Magnetic Field of a long solenoid
W_A < W_I
F = qv×B
B = µ0 I n
DS = 0 - dQ = 0 - P V^? = constant

11. Focal point of mirrror with curvature
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
F = R/2
Z²/n² (m_red/m_elec)
PdV +dU

12. Thermo: Adiabatic Work vs Isothermal Work
W_A < W_I
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Sin(?) = ?/d
(° of Freedom)kT/2

13. Boltzmann / Canonical distribution
NC?T
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
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
? = 5/3

14. Triplet/singlet states: symmetry and net spin
Q = CVexp(-t/RC)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
1/ne - where n is charge carrier density
ih_barL_z

15. Compton Scattering
?? = h/mc * (1-cos(?))
qvb = mv²/R
S_mean = s/Sqrt[N]
E = <?| H |?>

16. SR: Total Energy of a Particle
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
I = I_0 Cos[?]^2
F = qv×B

17. Ohm'S Law w/ current density
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
C_eq = (? 1/C_i)^-1
J = E s - s = Conductivity - E = Electric field

18. Gibbs Factor
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Dv = -udm/m - v = v0 + u ln(m0/m)
Exp(N(µ-e)/t)
µ = Current * Area T = µ x B

19. Radiation (Larmor - and another neat fact)
V = V0 + V0 a ?T
E²-p²c²
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Int ( A . dr) = Int ( del x A) dSurface

20. EM: Maxwell'S equations
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
I = -(c ?t)^2 + d^2
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
V(r) + L²2/2mr²

21. Bohr Model: Energy
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Measurements close to true value
Q = CVexp(-t/RC)
Z²/n² (m_red/m_elec)

22. Mech: Impulse
J = ? Fdt
F = I L X B
Ct²-x²-y²-z²
F = f* (c+v_r)/(c+v_s)

23. Rocket Equation
C_eq = (? 1/C_i)^-1
Cv = dE/dT = 3R
Dv = -udm/m - v = v0 + u ln(m0/m)
I_z = I_x + I_y (think hoop symmetry)

24. Relativistic length contraction
N²/Z (m_elec/m_red)
Measurements close to true value
L = L_0 Sqrt[1-v^2/c^2]
1/vLC

25. Induced EMF of solenoid
F = I L X B
N d flux / dt
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
L = T - V dL/dq = d/dt dL/dqdot

26. Mech: Virial Theorem
Int ( A . dr) = Int ( del x A) dSurface
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
<T> = -<V>/2
Z²/n² (m_red/m_elec)

27. Rayleigh'S Criterion
Braking Radiation
Sin(?) = ?/d
C = 4pe0 ab/(a-b) = inner and outer radii
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

28. Charge in Capacitor
Const: 2t = (n +.5)? Destructive 2t = n?
W_A < W_I
Q = CVexp(-t/RC)
Z = ?g_i*exp(-E/kT)

29. Perpendicular axis theorem
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
I_z = I_x + I_y (think hoop symmetry)
?~1/T
(3/2) n R ?t

30. Pauli matrices
? exp(-e/t)
F_f = µ*F_N
v(mean)
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

31. Delta Function Potential - type of WF
<?1|?2> = 0 ? Orthogonal
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
µ = Current * Area T = µ x B

32. Magnetic Field Through Ring
Ct²-x²-y²-z²
E = Z²*E1
µ0 I / 2R
V = -L di/dt

33. Stoke'S Theorem
Measurements close to true value
Int ( A . dr) = Int ( del x A) dSurface
?s = 0 - ?l = ±1
P/A = s T^4

34. Rocket Thrust
?~1/T
v(mean)
Isentropic
u dm/dt

35. Virial Theorem
? = h/mv
<T> = 1/2 * <dV/dx>
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
P/A = s T^4

36. First law of thermodynamics (explain direction of energy for each term)
A[B -C] + [A -C]B
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
E²-p²c²

37. Clausius-Clapeyron Equation
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Hbar*?³/(p²c³exp(hbar?/t)-1)
F = mv²/r
Dp/dt = L / (t ?V)

38. Atom: Positronium Reduced Mass
? = h/p
Z = ?g_i*exp(-E/kT)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
µ = m_e/2

39. Stefan-Boltzmann law for blackbodies (power per area and T)
1/ne - where n is charge carrier density
? exp(-e/t)
J = E s - s = Conductivity - E = Electric field
P/A = s T^4

40. SR: Spacetime Interval
P/A = s T^4
Sin(?) = ?/d
ds² = (c*dt)² - ?(x_i)²
Isentropic

41. Thermo: Monatomic gas ?=?
J = ? Fdt
Asin(?) = m?
? = 5/3
(3/2) n R ?t

42. Current in resistor in RC circuit
I = V/R exp(-t/RC)
P1V1 - P2V2 / (? - 1)
L = L_0 Sqrt[1-v^2/c^2]
Const: 2t = (n +.5)? Destructive 2t = n?

43. EM: SHO (Hooke)
ma + kx = 0
?mv
Braking Radiation
?max = 2.898 x 10 -³ / T

44. Mech: Parallel Axis Theorem (Moment of Inertia)
S = k ln[O] ; dS = dQ/T
PdV +dU
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
I = I_cm + md²

45. Adiabatic means
Isentropic
M? = 2dsin(?)
? = h/p
I = -(c ?t)^2 + d^2

46. Mean electron drift speed
µ = m_e/2
J/(ne) n: atom density
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Isentropic

47. Quant: Eigenvalue of Hermitian Operator
Exp(N(µ-e)/t)
Faraday/Lenz: current inducted opposes the changing field
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Always Real

48. Adiabatic processes (dS - dQ - P and V)
Cos[?] Sin[?] -Sin[?] Cos[?]
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
I = Im (sinc²(a)) ; a = pai sin(?) / ?
DS = 0 - dQ = 0 - P V^? = constant

49. Atom: Bohr Theory Ionization
ih_barL_z
DW/dq
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.
E = Z²*E1

50. Poisson distribution (µ and s)
µ=s^2
Asin(?) = m?
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
L = mr²d?/dt