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GRE Physics

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. Force exerted on charge by long wire
Braking Radiation
F = µ0 q v I / 2pr
X_L = i?L
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

2. Spherical Capacitor Equation
E = Z²*E1
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
C = 4pe0 ab/(a-b) = inner and outer radii
PdV +dU

3. Atom: Orbital Config
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
<?1|?2> = 0 ? Orthogonal
W_A < W_I
E²-p²c²

4. Entropy (# of states - and in terms of other thermo quantities)
S = k ln[O] ; dS = dQ/T
µ0 I / 2pR
E = <?| H |?>
I = I_0 Cos[?]^2

5. Bernoulli Equation
I = -(c ?t)^2 + d^2
v(mean)
P +1/2 ? v² + ?gh = Constant
J = E s - s = Conductivity - E = Electric field

6. Quant: [L_x -L_y] = ?
.5 LI²
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
ih_barL_z

7. Stark Effect
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
? = h/p
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
C = 4pe0 ab/(a-b) = inner and outer radii

8. Mech: Virial Theorem
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
F = s * T4
Z_c = -i/(?C) ; Z_L = i ? L
<T> = -<V>/2

9. Rayleigh'S Criterion
Exponentially decreasing radial function
?~1/T
Sin(?) = ?/d
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

10. Single Slit Diffraction Intensity
Cv = dE/dT = 3R
I = Im (sinc²(a)) ; a = pai sin(?) / ?
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
µ = Current * Area T = µ x B

11. Relativistic interval (which must remain constant for two events)
T^2 = k R^3 - k=constant
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 = -(c ?t)^2 + d^2
?_max = b/T

12. Compton Scattering
?? = h/mc * (1-cos(?))
J = E s - s = Conductivity - E = Electric field
1/ne - where n is charge carrier density
? = 5/3

13. Selection Rules
I_z = I_x + I_y (think hoop symmetry)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Always Real
?s = 0 - ?l = ±1

14. Lensmaker Equation - Thin Lens
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
I = I_cm + (1/2)m d^2
U = t^2 d/dt (logZ)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

15. Astro: p-p Chain
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
X_L = X_C or X_total = 0
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
4H + 2e- ? He +2? + 6?

16. Lab: Precision of Measurements
Measurements close to mean
F = s * T4
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
?max = 2.898 x 10 -³ / T

17. Invariant spatial quantity
F_f = µ*F_N
Ct²-x²-y²-z²
Dp/dt = L / (t ?V)
qvb = mv²/R

18. Energy in terms of partition function
F_f = µ*F_N
U = t^2 d/dt (logZ)
Dp/dt = L / (t ?V)
Q = CVexp(-t/RC)

19. Mean electron drift speed
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
J/(ne) n: atom density
I = V/R exp(-t/RC)

20. Quant: Eigenvalue of Hermitian Operator
Infinitely close to equilibrium at all times
Always Real
I = V/R exp(-t/RC)
I = Im (sinc²(a)) ; a = pai sin(?) / ?

21. Atom: Hydrogen Wave Function Type
(3/2) n R ?t
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Exponentially decreasing radial function

22. EM: Series Capacitance
C_eq = (? 1/C_i)^-1
Z = ?g_i*exp(-E/kT)
ds² = (c*dt)² - ?(x_i)²
(3/2) n R ?t

23. Work done on a gas
Measurements close to true value
Opposing charge induced upon conductor
ds² = (c*dt)² - ?(x_i)²
DW = P dV

24. Mech: Force of Friction
F_f = µ*F_N
Braking Radiation
I ' = I cos²(?)
E²-p²c²

25. EM: SHO (Hooke)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
X_L = X_C or X_total = 0
ma + kx = 0
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

26. Rotation matrix (2x2)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Cos[?] Sin[?] -Sin[?] Cos[?]
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
ma + kx = 0

27. Magnetic Dipole Moment and Torque
Sin(?) = ?/d
I_z = I_x + I_y (think hoop symmetry)
µ = Current * Area T = µ x B
J = E s - s = Conductivity - E = Electric field

28. Electromotive Force
Dp/dt = L / (t ?V)
DW/dq
N d flux / dt
I = I_cm + (1/2)m d^2

29. Virial Theorem
<T> = 1/2 * <dV/dx>
V = -L di/dt
Cos[?] Sin[?] -Sin[?] Cos[?]
C = 4pe0 ab/(a-b) = inner and outer radii

30. Relativistic length contraction
µ0 I / 2R
Measurements close to mean
L = L_0 Sqrt[1-v^2/c^2]
? = 1.22?/D

31. Bohr Model: Energy
Z²/n² (m_red/m_elec)
?max = 2.898 x 10 -³ / T
C_eq = (? 1/C_i)^-1
Cv = dE/dT = 3R

32. Resistance - length - area - rho
F = qv×B
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
I = -(c ?t)^2 + d^2
X_C = 1/(i?C)

33. Delta Function Potential - type of WF
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Braking Radiation
M? = 2dsin(?)
(3/2) n R ?t

34. SR: Total Energy of a Particle
L = T - V dL/dq = d/dt dL/dqdot
? = h/p
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
F = qv×B

35. Rayleigh criterion
Exponentially decreasing radial function
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
I = I_cm + (1/2)m d^2
? = 1.22? / d

36. Atom: Bohr Formula
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
S = k ln[O] ; dS = dQ/T
H = H_0 + ?H

37. EM: Method of Images
Opposing charge induced upon conductor
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
PdV +dU
DS = 0 - dQ = 0 - P V^? = constant

38. Parallel axis theorem
L = T - V dL/dq = d/dt dL/dqdot
I = I_cm + (1/2)m d^2
ih_barL_z
S_mean = s/Sqrt[N]

39. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Measurements close to mean
L = mr²d?/dt
1/vLC

40. Atom: Bohr Theory Ionization
V = V0 + V0 a ?T
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
E = Z²*E1
? (t-vx/c²)

41. Time Lorentz Transformation
? (t-vx/c²)
J/(ne) n: atom density
Braking Radiation
.5 LI²

42. EM: Electromagnetic inertia
PdV +dU
E = <?| H |?>
?= h/v(2mE)
Faraday/Lenz: current inducted opposes the changing field

43. Thermo: Adiabatic Work vs Isothermal Work
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
(3/2) n R ?t
J/(ne) n: atom density
W_A < W_I

44. Malus Law

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45. Coriolis Force
?s = 0 - ?l = ±1
F = -2*m(? x r)
DS = 0 - dQ = 0 - P V^? = constant
J/(ne) n: atom density

46. QM: de Broglie Wavelength
?= h/v(2mE)
A[B -C] + [A -C]B
I = I_0 Cos[?]^2
4H + 2e- ? He +2? + 6?

47. Thermo: 1st Law
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.
1/vLC
?~T
dQ = dW +dU

48. Lagrangian and Lagrange'S equation
L = T - V dL/dq = d/dt dL/dqdot
?mv
?max = 2.898 x 10 -³ / T
u dm/dt

49. Angular momentum - Central Force Motion
? = ?0 root((1-v/c)/(1+v/c))
NC?T
L = mr²d?/dt
Asin(?) = m?

50. 3 Laws of Thermo
.5 LI²
Sin(?) = ?/d
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...