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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. Thermo: Adiabatic Work vs Isothermal Work
L = mr²d?/dt
W_A < W_I
C = 4pe0 ab/(a-b) = inner and outer radii
Const: 2t = (n +.5)? Destructive 2t = n?

2. Work (P - V)
S_mean = s/Sqrt[N]
P1V1 - P2V2 / (? - 1)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
µ0 I1I2 / (2pd)

3. Pauli matrices
dQ = dW +dU
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(?)
J/(ne) n: atom density

4. RLC resonance condition
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
I = I_cm + (1/2)m d^2
F = I L X B

5. Bernoulli Equation
P +1/2 ? v² + ?gh = Constant
I = V/R exp(-t/RC)
F = -2*m(? x r)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

6. Magnetic Dipole Moment and Torque
µ = Current * Area T = µ x B
Dv = -udm/m - v = v0 + u ln(m0/m)
F = s * T4
<?|O|?>

7. Stefan-Boltzmann law for blackbodies (power per area and T)
0
W_A < W_I
L = T - V dL/dq = d/dt dL/dqdot
P/A = s T^4

8. Doppler Shift for light
J = ? Fdt
I = I_0 Cos[?]^2
? = ?0 root((1-v/c)/(1+v/c))
I ' = I cos²(?)

9. Malus Law

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10. Work done on a gas
?_max = b/T
DW = P dV
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
A[B -C] + [A -C]B

11. Magnetic field due to a segment of wire
<T> = -<V>/2
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
? exp(-e/t)

12. Stoke'S Theorem
? = 1.22?/D
Int ( A . dr) = Int ( del x A) dSurface
1/ne - where n is charge carrier density
I = I_cm + (1/2)m d^2

13. Atom: Bohr Formula
U - ts = -tlog(Z)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Dv = -udm/m - v = v0 + u ln(m0/m)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

14. Source-free RC Circuit
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
F = f* (c+v_r)/(c+v_s)
ih_barL_z

15. Magnetic Field For Current in Long Wire
ds² = (c*dt)² - ?(x_i)²
X_L = i?L
<T> = -<V>/2
µ0 I / 2pR

16. Boltzmann / Canonical distribution
Ct²-x²-y²-z²
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
F = -2*m(? x r)
F = qv×B

17. Doppler Shift in Frequency
Always Real
F = qv×B
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
F = f* (c+v_r)/(c+v_s)

18. Doppler shift for light
T = I?²/2
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
F = µ0 q v I / 2pr
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

19. Entropy (# of states - and in terms of other thermo quantities)
S = k ln[O] ; dS = dQ/T
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.
I = I_0 Cos[?]^2
Measurements close to mean

20. A reversible process stays..
Infinitely close to equilibrium at all times
Sin(?) = ?/d
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
?s = 0 - ?l = ±1

21. Induced EMF of solenoid
v(mean)
X_L = X_C or X_total = 0
Asin(?) = m?
N d flux / dt

22. QM: de Broglie Wavelength
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
?= h/v(2mE)
Isentropic
I = -(c ?t)^2 + d^2

23. Energy in terms of partition function
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
X_L = X_C or X_total = 0
U = t^2 d/dt (logZ)
Q = CVexp(-t/RC)

24. Mech: Parallel Axis Theorem (Moment of Inertia)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Dv = -udm/m - v = v0 + u ln(m0/m)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
I = I_cm + md²

25. Single Slit Diffraction Maximum
Asin(?) = m?
I = I_cm + md²
V(r) + L²2/2mr²
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

26. Lab: Precision of Measurements
Measurements close to mean
E = <?| H |?>
dU = 0 ? dS = ?dW/T
J = E s - s = Conductivity - E = Electric field

27. Planck Radiation Law
.5 CV²
Hbar*?³/(p²c³exp(hbar?/t)-1)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
KE = 1/2 * µ (dr/dt)² L = µ r x v

28. Perturbations
H = H_0 + ?H
T^2 = k R^3 - k=constant
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

29. Rocket Thrust
u dm/dt
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
N²/Z (m_elec/m_red)

30. Energy levels from the Coulomb potential
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.
Faraday/Lenz: current inducted opposes the changing field
C_eq = ?C_i

31. Perpendicular axis theorem
I_z = I_x + I_y (think hoop symmetry)
F = s * T4
W_A < W_I
DW/dq

32. Coriolis Force
qvb = mv²/R
F = -2*m(? x r)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
T = I?²/2

33. Wein'S Displacement Law
DS = 0 - dQ = 0 - P V^? = constant
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
I = Im (sinc²(a)) ; a = pai sin(?) / ?
?max = 2.898 x 10 -³ / T

34. Mech: Force of Friction
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
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
F_f = µ*F_N
Isentropic

35. Triplet/singlet states: symmetry and net spin
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Z_c = -i/(?C) ; Z_L = i ? L
?? = h/mc * (1-cos(?))
A[B -C] + [A -C]B

36. Spherical Capacitor Equation
Opposing charge induced upon conductor
µ0 I / 2R
C = 4pe0 ab/(a-b) = inner and outer radii
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

37. Parallel axis theorem
Infinitely close to equilibrium at all times
<T> = -<V>/2
Isentropic
I = I_cm + (1/2)m d^2

38. Rotation matrix (2x2)
Cos[?] Sin[?] -Sin[?] Cos[?]
1/ne - where n is charge carrier density
E = <?| H |?>
H = H_0 + ?H

39. Selection Rules
J = ? Fdt
Braking Radiation
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
?s = 0 - ?l = ±1

40. Thin Film Theory: Constructive / Destructive Interference
?mc²
Const: 2t = (n +.5)? Destructive 2t = n?
Cv = dE/dT = 3R
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

41. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
F = s * T4
Measurements close to true value
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
(3/2) n R ?t

42. Quant: Expectation Value
1/vLC
F = mv²/r
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
<?|O|?>

43. Polarizers - intensity when crossed at ?
ma + kx = 0
S = k ln[O] ; dS = dQ/T
(° of Freedom)kT/2
I = I_0 Cos[?]^2

44. Kepler'S third law (T and R)
qvb = mv²/R
A[B -C] + [A -C]B
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
T^2 = k R^3 - k=constant

45. Mech: Virial Theorem
? (t-vx/c²)
<T> = -<V>/2
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
µ0 I / 2R

46. EM: Maxwell'S equations
I = V/R exp(-t/RC)
? = 1.22? / d
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Asin(?) = m?

47. Relativistic length contraction
Exponentially decreasing radial function
L = L_0 Sqrt[1-v^2/c^2]
E²-p²c²
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

48. E field of a capacitor (d->0)
X_L = X_C or X_total = 0
Sin(?) = ?/d
E = s/e_0
Cv = dE/dT = 3R

49. Dulong Petit Law
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
? = 1.22?/D
Cv = dE/dT = 3R
J = ? Fdt

50. SR: Spacetime Interval
I = I_0 Cos[?]^2
P1V1 - P2V2 / (? - 1)
ds² = (c*dt)² - ?(x_i)²
v(mean)