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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. Bar magnets -- direction of B field lines - earth'S B field
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
1/vLC
C = 4pe0 ab/(a-b) = inner and outer radii
U - ts = -tlog(Z)

2. Solid: Resistivity of Semi-Conductor
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Braking Radiation
?mc²
?~1/T

3. E field of a capacitor (d->0)
N²/Z (m_elec/m_red)
B = µ0 I n
E = s/e_0
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

4. Dulong Petit Law
Cv = dE/dT = 3R
? = ?0 root((1-v/c)/(1+v/c))
1/vLC
Hbar*?³/(p²c³exp(hbar?/t)-1)

5. Atom: Bohr Theory Ionization
Exponentially decreasing radial function
E = Z²*E1
P/A = s T^4
1/ne - where n is charge carrier density

6. Error in the mean if each measurement has the same uncertainty s
1/vLC
S_mean = s/Sqrt[N]
DW = P dV
I = V/R exp(-t/RC)

7. Force/length between two wires
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
NC?T
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
µ0 I1I2 / (2pd)

8. Single Slit Diffraction Maximum
E = <?| H |?>
KE = 1/2 * µ (dr/dt)² L = µ r x v
ma + kx = 0
Asin(?) = m?

9. Atom: Positronium Reduced Mass
X_L = X_C or X_total = 0
T^2 = k R^3 - k=constant
qvb = mv²/R
µ = m_e/2

10. Astro: Aperture Formula (Rayleigh Criterion)
W_A < W_I
? = h/mv
? = 1.22?/D
(3/2) n R ?t

11. Relativistic interval (which must remain constant for two events)
? = h/p
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
?max = 2.898 x 10 -³ / T
I = -(c ?t)^2 + d^2

12. Inductance of Solenoid
J = ? Fdt
Sin(?) = ?/d
0
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

13. Quant: Eigenvalue of Hermitian Operator
(3/2) n R ?t
Always Real
Infinitely close to equilibrium at all times
?_max = b/T

14. Selection rules for atomic transitions
µ=s^2
W_A < W_I
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

15. Quant: Commutator Relation [AB -C]
C_eq = (? 1/C_i)^-1
Braking Radiation
A[B -C] + [A -C]B
W_A < W_I

16. Focal point of mirrror with curvature
F = R/2
E²-p²c²
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
S = k ln[O] ; dS = dQ/T

17. Induced EMF of solenoid
N d flux / dt
dU = 0 ? dS = ?dW/T
Dp/dt = L / (t ?V)
ma + kx = 0

18. Weighted average (mean and unc. of mean)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
DS = 0 - dQ = 0 - P V^? = constant
Cos[?] Sin[?] -Sin[?] Cos[?]
µ = m_e/2

19. Entropy (# of states - and in terms of other thermo quantities)
J = E s - s = Conductivity - E = Electric field
DW/dq
? = ?0 root((1-v/c)/(1+v/c))
S = k ln[O] ; dS = dQ/T

20. EM: Parallel Capacitance
1/ne - where n is charge carrier density
C_eq = ?C_i
Exp(N(µ-e)/t)
M? = 2dsin(?)

21. Quant: Orthogonality of States
I ' = I cos²(?)
Const: 2t = (n +.5)? Destructive 2t = n?
<?1|?2> = 0 ? Orthogonal
?= h/v(2mE)

22. Thermo: Monatomic gas ?=?
Z_c = -i/(?C) ; Z_L = i ? L
<T> = -<V>/2
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
? = 5/3

23. Perturbations
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
P² ~ R³
H = H_0 + ?H
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

24. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
?= h/v(2mE)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

25. Mech: Parallel Axis Theorem (Moment of Inertia)
H = H_0 + ?H
1/ne - where n is charge carrier density
Cv = dE/dT = 3R
I = I_cm + md²

26. A reversible process stays..
Infinitely close to equilibrium at all times
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
F = mv²/r
<T> = -<V>/2

27. Thin Film Theory: Constructive / Destructive Interference
U = t^2 d/dt (logZ)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Const: 2t = (n +.5)? Destructive 2t = n?
ds² = (c*dt)² - ?(x_i)²

28. Bohr Model: Energy
<T> = -<V>/2
Int ( A . dr) = Int ( del x A) dSurface
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Z²/n² (m_red/m_elec)

29. Lab: Accuracy of Measurements
DW = P dV
Measurements close to true value
Isentropic
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

30. Adiabatic processes (dS - dQ - P and V)
NC?T
DS = 0 - dQ = 0 - P V^? = constant
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

31. Double Slit: Interference Minimum - Diffraction Minimum
V = V0 + V0 a ?T
I = I_cm + (1/2)m d^2
S = k ln[O] ; dS = dQ/T
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

32. Relativistic length contraction
I = I_cm + md²
Opposing charge induced upon conductor
L = L_0 Sqrt[1-v^2/c^2]
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

33. Relativistic Energy
?mc²
dQ = dW +dU
µ=s^2
? = 5/3

34. Springs in series/parallel
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
µ0 I / 2pR
I = -(c ?t)^2 + d^2
C = 4pe0 ab/(a-b) = inner and outer radii

35. Work (P - V)
Asin(?) = m?
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
P1V1 - P2V2 / (? - 1)
Exponentially decreasing radial function

36. Energy in a Capacitor
(3/2) n R ?t
N²/Z (m_elec/m_red)
N d flux / dt
.5 CV²

37. Energy in terms of partition function
KE = 1/2 * µ (dr/dt)² L = µ r x v
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
U = t^2 d/dt (logZ)
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.

38. Partition Function
M? = 2dsin(?)
I = I_cm + md²
? exp(-e/t)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

39. Invariant spatial quantity
L = L_0 Sqrt[1-v^2/c^2]
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
I = V/R exp(-t/RC)
Ct²-x²-y²-z²

40. Electromotive Force
V = V0 + V0 a ?T
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
C = 4pe0 ab/(a-b) = inner and outer radii
DW/dq

41. Doppler Shift for light
? = ?0 root((1-v/c)/(1+v/c))
Asin(?) = m?
V = V0 + V0 a ?T
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

42. Expectation value of the energy of state |?>
Cv = dE/dT = 3R
PdV +dU
E = <?| H |?>
NC?T

43. Effective Potential
V(r) + L²2/2mr²
PdV +dU
P1V1 - P2V2 / (? - 1)
Cv = dE/dT = 3R

44. Radiation (Larmor - and another neat fact)
F = qv×B
PdV +dU
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
S = k ln[O] ; dS = dQ/T

45. 3 Laws of Thermo
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
V(r) + L²2/2mr²
(° of Freedom)kT/2
?= h/v(2mE)

46. Delta Function Potential - type of WF
J/(ne) n: atom density
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
ih_barL_z
Hbar*?³/(p²c³exp(hbar?/t)-1)

47. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
T = I?²/2
Asin(?) = m?

48. Thermo: Isothermal
dU = 0 ? dS = ?dW/T
KE = 1/2 * µ (dr/dt)² L = µ r x v
L = T - V dL/dq = d/dt dL/dqdot
1/vLC

49. Rocket Equation
M? = 2dsin(?)
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
Dv = -udm/m - v = v0 + u ln(m0/m)
?? = h/mc * (1-cos(?))

50. Helmholtz Free Energy
U - ts = -tlog(Z)
L = mr²d?/dt
?~T
Asin(?) = m?