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GRE Physics

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Answer 50 questions in 15 minutes.
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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. Single Slit Diffraction Maximum
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
I ' = I cos²(?)
Asin(?) = m?
?_max = b/T

2. Mech: Parallel Axis Theorem (Moment of Inertia)
I = I_cm + md²
I = -(c ?t)^2 + d^2
? = h/p
Asin(?) = m?

3. Weighted average (mean and unc. of mean)
W_A < W_I
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Cos[?] Sin[?] -Sin[?] Cos[?]

4. Magnetic Field Through Ring
<?|O|?>
A[B -C] + [A -C]B
µ0 I / 2R
T = I?²/2

5. EM: Electric Field inside of Conductor
Z_c = -i/(?C) ; Z_L = i ? L
Exponentially decreasing radial function
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
0

6. Force exerted on charge by long wire
F = µ0 q v I / 2pr
Exponentially decreasing radial function
H = H_0 + ?H
L = T - V dL/dq = d/dt dL/dqdot

7. Springs in series/parallel
ih_barL_z
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
V = V0 + V0 a ?T
Always Real

8. Stefan-Boltzmann law for blackbodies (power per area and T)
KE = 1/2 * µ (dr/dt)² L = µ r x v
qvb = mv²/R
P/A = s T^4
F_f = µ*F_N

9. Invariant Energy Quantity
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Ct²-x²-y²-z²
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
E²-p²c²

10. QM: de Broglie Wavelength
?= h/v(2mE)
1/ne - where n is charge carrier density
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.
N²/Z (m_elec/m_red)

11. Doppler Shift in Frequency
S_mean = s/Sqrt[N]
F = f* (c+v_r)/(c+v_s)
? (t-vx/c²)
E²-p²c²

12. Rocket Equation
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
µ0 I / 2pR
J/(ne) n: atom density
Dv = -udm/m - v = v0 + u ln(m0/m)

13. Delta Function Potential - type of WF
Z²/n² (m_red/m_elec)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
F = mv²/r

14. Energy in terms of partition function
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
E = <?| H |?>
U = t^2 d/dt (logZ)
NC?T

15. td(entropy) =
X_C = 1/(i?C)
J = ? Fdt
.5 CV²
PdV +dU

16. EM: Electromagnetic inertia
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Faraday/Lenz: current inducted opposes the changing field
Z_c = -i/(?C) ; Z_L = i ? L
V(r) + L²2/2mr²

17. Relativistic Momentum
Z = ?g_i*exp(-E/kT)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
?mv
F = I L X B

18. Relativistic interval (which must remain constant for two events)
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.
?? = h/mc * (1-cos(?))
I = -(c ?t)^2 + d^2
Dp/dt = L / (t ?V)

19. Quant: Commutator Relation [AB -C]
A[B -C] + [A -C]B
DS = 0 - dQ = 0 - P V^? = constant
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Dv = -udm/m - v = v0 + u ln(m0/m)

20. Selection rules for atomic transitions
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Opposing charge induced upon conductor
I = I_cm + (1/2)m d^2

21. E field of a capacitor (d->0)
Measurements close to mean
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
E = s/e_0
.5 LI²

22. EM: Maxwell'S equations
?mc²
.5 LI²
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
µ0 I1I2 / (2pd)

23. Law of Mass Action
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
F = qv×B
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

24. Thermo: Adiabatic Work vs Isothermal Work
W_A < W_I
4H + 2e- ? He +2? + 6?
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

25. Force on a wire in magnetic field
F = I L X B
I = Im (sinc²(a)) ; a = pai sin(?) / ?
DW = P dV
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

26. Error in the mean if each measurement has the same uncertainty s
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.
S_mean = s/Sqrt[N]
0
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

27. Quant: Expectation Value
? exp(-e/t)
Const: 2t = (n +.5)? Destructive 2t = n?
<?|O|?>
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

28. Polarizers - intensity when crossed at ?
I = I_0 Cos[?]^2
?~T
V(r) + L²2/2mr²
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.

29. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Faraday/Lenz: current inducted opposes the changing field
4H + 2e- ? He +2? + 6?
E = s/e_0

30. Solid: Resistivity of Semi-Conductor
E = Z²*E1
Dv = -udm/m - v = v0 + u ln(m0/m)
?~1/T
Measurements close to true value

31. Rotation matrix (2x2)
v(mean)
I = I_cm + (1/2)m d^2
µ0 I1I2 / (2pd)
Cos[?] Sin[?] -Sin[?] Cos[?]

32. Atom: Bohr Formula
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
? = ?0 root((1-v/c)/(1+v/c))
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.
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

33. Solid: Resistivity of Metal
? (t-vx/c²)
1/vLC
S_mean = s/Sqrt[N]
?~T

34. Charge in Capacitor
I = -(c ?t)^2 + d^2
Q = CVexp(-t/RC)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

35. Thermo: Average Total Energy
I = I_0 Cos[?]^2
(° of Freedom)kT/2
Cv = dE/dT = 3R
KE = 1/2 * µ (dr/dt)² L = µ r x v

36. Kepler'S Three Laws
ds² = (c*dt)² - ?(x_i)²
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
0
H = H_0 + ?H

37. Magnetic Field For Current in Long Wire
u dm/dt
µ0 I / 2pR
1/ne - where n is charge carrier density
A[B -C] + [A -C]B

38. Current in resistor in RC circuit
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
?s = 0 - ?l = ±1
?mc²
I = V/R exp(-t/RC)

39. Helmholtz Free Energy
C = 4pe0 ab/(a-b) = inner and outer radii
<T> = -<V>/2
U - ts = -tlog(Z)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

40. Parallel axis theorem
?mv
I = I_cm + (1/2)m d^2
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
ih_barL_z

41. Self Inductance
ih_barL_z
V = -L di/dt
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
S_mean = s/Sqrt[N]

42. Lab: Accuracy of Measurements
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Measurements close to true value
S = k ln[O] ; dS = dQ/T
v(mean)

43. Atom: Bohr Theory Ionization
<?1|?2> = 0 ? Orthogonal
E = Z²*E1
Infinitely close to equilibrium at all times
Q = CVexp(-t/RC)

44. Atom: Hydrogen Wave Function Type
?mc²
Exponentially decreasing radial function
ds² = (c*dt)² - ?(x_i)²
.5 LI²

45. Partition Function
? exp(-e/t)
? = 1.22? / d
?~T
Z = ?g_i*exp(-E/kT)

46. De Broglie wavelength
v(mean)
? = h/p
Asin(?) = m?
µ0 I1I2 / (2pd)

47. Focal point of mirrror with curvature
u dm/dt
ds² = (c*dt)² - ?(x_i)²
µ0 I1I2 / (2pd)
F = R/2

48. Planck Radiation Law
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
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
X_L = i?L
Hbar*?³/(p²c³exp(hbar?/t)-1)

49. Lab: Standard Deviation of Poisson
ih_barL_z
U - ts = -tlog(Z)
E = Z²*E1
v(mean)

50. Quant: [L_x -L_y] = ?
N d flux / dt
Infinitely close to equilibrium at all times
ih_barL_z
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

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