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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. Coriolis Force
F = -2*m(? x r)
H = H_0 + ?H
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
µ = Current * Area T = µ x B

2. Lab: Standard Deviation of Poisson
I = -(c ?t)^2 + d^2
A[B -C] + [A -C]B
v(mean)
NC?T

3. Rocket Thrust
F = mv²/r
u dm/dt
Faraday/Lenz: current inducted opposes the changing field
I = I_0 Cos[?]^2

4. Atom: Hydrogen Wave Function Type
Exponentially decreasing radial function
Hbar*?³/(p²c³exp(hbar?/t)-1)
T = I?²/2
0

5. Lab: Accuracy of Measurements
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
PdV +dU
Measurements close to true value

6. Thermo: Adiabatic Work vs Isothermal Work
Always Real
Measurements close to true value
W_A < W_I
?s = 0 - ?l = ±1

7. Thermo: Partition Function
P/A = s T^4
Z = ?g_i*exp(-E/kT)
N d flux / dt
I = I_cm + md²

8. First law of thermodynamics (explain direction of energy for each term)
X_C = 1/(i?C)
4H + 2e- ? He +2? + 6?
<T> = 1/2 * <dV/dx>
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

9. Center of Mass: Kinetic Energy & Angular Momentum
1/2 CV²
X_L = i?L
KE = 1/2 * µ (dr/dt)² L = µ r x v
P1V1 - P2V2 / (? - 1)

10. Thermo: Monatomic gas ?=?
? = 5/3
E = <?| H |?>
<?|O|?>
1/ne - where n is charge carrier density

11. SR: Total Energy of a Particle
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
T^2 = k R^3 - k=constant
ma + kx = 0
?s = 0 - ?l = ±1

12. Time Lorentz Transformation
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
F = s * T4
H = H_0 + ?H
? (t-vx/c²)

13. Thermo: Isothermal
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Q = CVexp(-t/RC)
dU = 0 ? dS = ?dW/T
?? = h/mc * (1-cos(?))

14. Lagrangian and Lagrange'S equation
F = µ0 q v I / 2pr
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
L = T - V dL/dq = d/dt dL/dqdot

15. Mech: Virial Theorem
W_A < W_I
L = L_0 Sqrt[1-v^2/c^2]
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
<T> = -<V>/2

16. Compton Scattering
?? = h/mc * (1-cos(?))
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Hbar*?³/(p²c³exp(hbar?/t)-1)
J/(ne) n: atom density

17. Force exerted on charge by long wire
F = µ0 q v I / 2pr
L = T - V dL/dq = d/dt dL/dqdot
T = I?²/2
? = h/p

18. Bar magnets -- direction of B field lines - earth'S B field
ds² = (c*dt)² - ?(x_i)²
Dp/dt = L / (t ?V)
F_f = µ*F_N
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

19. Radiation (Larmor - and another neat fact)
P² ~ R³
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
<?|O|?>
.5 LI²

20. Resonance frequency of LC circuit
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
1/vLC
Dv = -udm/m - v = v0 + u ln(m0/m)
? = h/p

21. Relativistic length contraction
1/2 CV²
Dp/dt = L / (t ?V)
µ0 I1I2 / (2pd)
L = L_0 Sqrt[1-v^2/c^2]

22. Triplet/singlet states: symmetry and net spin
L = T - V dL/dq = d/dt dL/dqdot
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
1/2 CV²
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

23. SR: Spacetime Interval
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
ds² = (c*dt)² - ?(x_i)²
DW = P dV
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

24. Wein'S displacement law for blackbodies (? and T)
Isentropic
DS = 0 - dQ = 0 - P V^? = constant
F = I L X B
?_max = b/T

25. Magnetic Dipole Moment and Torque
? = 1.22?/D
µ = Current * Area T = µ x B
W_A < W_I
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

26. Adiabatic processes (dS - dQ - P and V)
PdV +dU
U - ts = -tlog(Z)
DS = 0 - dQ = 0 - P V^? = constant
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

27. EM: AC Resonance
? = 1.22?/D
X_L = X_C or X_total = 0
F = µ0 q v I / 2pr
F = -2*m(? x r)

28. RLC resonance condition
<T> = -<V>/2
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
? = 1.22? / d
F_f = µ*F_N

29. E field of a capacitor (d->0)
V = -L di/dt
V(r) + L²2/2mr²
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
E = s/e_0

30. Stefan-Boltzmann law for blackbodies (power per area and T)
A[B -C] + [A -C]B
B = µ0 I n
?mv
P/A = s T^4

31. Source-free RC Circuit
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
T = I?²/2
PdV +dU
? = ?0 root((1-v/c)/(1+v/c))

32. Angular momentum operators L^2 and L_z
I_z = I_x + I_y (think hoop symmetry)
I ' = I cos²(?)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
I = Im (sinc²(a)) ; a = pai sin(?) / ?

33. Partition Function
Const: 2t = (n +.5)? Destructive 2t = n?
X_L = i?L
? exp(-e/t)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

34. Self Inductance
<T> = 1/2 * <dV/dx>
?~T
V = -L di/dt
C = 4pe0 ab/(a-b) = inner and outer radii

35. Force/length between two wires
E = s/e_0
v(mean)
µ0 I1I2 / (2pd)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

36. EM: Reactance of Inductor
U - ts = -tlog(Z)
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.
L = L_0 Sqrt[1-v^2/c^2]
X_L = i?L

37. Clausius-Clapeyron Equation
Dp/dt = L / (t ?V)
?~T
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
?mv

38. Astro: Kepler'S Third Law
Braking Radiation
P² ~ R³
PdV +dU
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

39. Ohm'S Law w/ current density
F_f = µ*F_N
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
J = E s - s = Conductivity - E = Electric field

40. Quant: Commutator Relation [AB -C]
ma + kx = 0
A[B -C] + [A -C]B
<?1|?2> = 0 ? Orthogonal
Opposing charge induced upon conductor

41. Magnetic Field For Current in Long Wire
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
F = s * T4
µ0 I / 2pR

42. Law of Mass Action
Const: 2t = (n +.5)? Destructive 2t = n?
Int ( A . dr) = Int ( del x A) dSurface
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

43. Mech: Impulse
J = E s - s = Conductivity - E = Electric field
.5 CV²
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
J = ? Fdt

44. Quant: Eigenvalue of Hermitian Operator
Always Real
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 = I_cm + md²
Hbar*?³/(p²c³exp(hbar?/t)-1)

45. Doppler Shift for light
? = ?0 root((1-v/c)/(1+v/c))
V = -L di/dt
µ = Current * Area T = µ x B
ma + kx = 0

46. Hall Coefficient
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
ma + kx = 0
1/ne - where n is charge carrier density

47. Solid: Resistivity of Metal
Q = CVexp(-t/RC)
S_mean = s/Sqrt[N]
?~T
DW = P dV

48. Boltzmann / Canonical distribution
Exp(N(µ-e)/t)
F = qv×B
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
W_A < W_I

49. How to derive cylcotron frequency
qvb = mv²/R
I = Im (sinc²(a)) ; a = pai sin(?) / ?
µ=s^2
?= h/v(2mE)

50. Wein'S Displacement Law
?max = 2.898 x 10 -³ / T
Exp(N(µ-e)/t)
µ0 I / 2pR
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