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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. Double Slit: Interference Minimum - Diffraction Minimum
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
<T> = -<V>/2

2. Relativistic Energy
?mc²
Z²/n² (m_red/m_elec)
F_f = µ*F_N
E = s/e_0

3. Bar magnets -- direction of B field lines - earth'S B field
µ = m_e/2
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
v(mean)

4. Lab: Accuracy of Measurements
F = qv×B
Measurements close to true value
PdV +dU
Hbar*?³/(p²c³exp(hbar?/t)-1)

5. QM: de Broglie Wavelength
NC?T
?= h/v(2mE)
? = 5/3
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

6. Wein'S displacement law for blackbodies (? and T)
ds² = (c*dt)² - ?(x_i)²
? = 5/3
dQ = dW +dU
?_max = b/T

7. Helmholtz Free Energy
F = I L X B
W_A < W_I
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.
U - ts = -tlog(Z)

8. Commutator identities ( [B -A C] - [A -B] )
C_eq = ?C_i
L = L_0 Sqrt[1-v^2/c^2]
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Cos[?] Sin[?] -Sin[?] Cos[?]

9. Partition Function
X_C = 1/(i?C)
Ct²-x²-y²-z²
? exp(-e/t)
Hbar*?³/(p²c³exp(hbar?/t)-1)

10. Thermo: Blackbody Radiation
F = s * T4
DS = 0 - dQ = 0 - P V^? = constant
F = -2*m(? x r)
F = f* (c+v_r)/(c+v_s)

11. EM: Bremsstrahlung (translation)
Braking Radiation
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Faraday/Lenz: current inducted opposes the changing field
L = mr²d?/dt

12. Work (P - V)
P1V1 - P2V2 / (? - 1)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
? exp(-e/t)

13. Stoke'S Theorem
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Int ( A . dr) = Int ( del x A) dSurface
U - ts = -tlog(Z)
Infinitely close to equilibrium at all times

14. Malus Law

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15. Ohm'S Law w/ current density
1/2 CV²
J = E s - s = Conductivity - E = Electric field
? exp(-e/t)
Const: 2t = (n +.5)? Destructive 2t = n?

16. Solid: Resistivity of Metal
F = qv×B
?~T
µ0 I / 2R
F = µ0 q v I / 2pr

17. Mech: Force of Friction
µ=s^2
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
M? = 2dsin(?)
F_f = µ*F_N

18. Atom: Orbital Config
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
J/(ne) n: atom density
T^2 = k R^3 - k=constant
µ0 I / 2pR

19. Rayleigh criterion
<?1|?2> = 0 ? Orthogonal
V(r) + L²2/2mr²
µ0 I / 2pR
? = 1.22? / d

20. Pauli matrices
Z²/n² (m_red/m_elec)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
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
dQ = dW +dU

21. Mech: Virial Theorem
<T> = -<V>/2
DW = P dV
E = <?| H |?>
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

22. Stefan-Boltzmann law for blackbodies (power per area and T)
J/(ne) n: atom density
P/A = s T^4
Ct²-x²-y²-z²
?s = 0 - ?l = ±1

23. Springs in series/parallel
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
E²-p²c²
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

24. Relativistic length contraction
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
L = L_0 Sqrt[1-v^2/c^2]
<T> = 1/2 * <dV/dx>
W_A < W_I

25. Doppler shift for light
qvb = mv²/R
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
E²-p²c²

26. Mech: Impulse
L = L_0 Sqrt[1-v^2/c^2]
J = ? Fdt
F = s * T4
?? = h/mc * (1-cos(?))

27. EM: Series Capacitance
F_f = µ*F_N
µ0 I1I2 / (2pd)
C_eq = (? 1/C_i)^-1
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

28. Stark Effect
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/T
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
?_max = b/T

29. Doppler Shift in Frequency
? = h/mv
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
? = 1.22? / d
F = f* (c+v_r)/(c+v_s)

30. Electromotive Force
F = s * T4
DW/dq
?mv
? = ?0 root((1-v/c)/(1+v/c))

31. First law of thermodynamics (explain direction of energy for each term)
L = T - V dL/dq = d/dt dL/dqdot
I = Im (sinc²(a)) ; a = pai sin(?) / ?
dU = 0 ? dS = ?dW/T
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

32. Clausius-Clapeyron Equation
.5 CV²
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
H = H_0 + ?H
Dp/dt = L / (t ?V)

33. Virial Theorem
<T> = 1/2 * <dV/dx>
? = h/mv
V = V0 + V0 a ?T
qvb = mv²/R

34. Energy in a Capacitor
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
DS = 0 - dQ = 0 - P V^? = constant
.5 CV²
I = V/R exp(-t/RC)

35. E field of a capacitor (d->0)
I ' = I cos²(?)
S = k ln[O] ; dS = dQ/T
(3/2) n R ?t
E = s/e_0

36. Addition of relativistic velocities

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37. Thermo: Average Total Energy
C = 4pe0 ab/(a-b) = inner and outer radii
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
I_z = I_x + I_y (think hoop symmetry)
(° of Freedom)kT/2

38. Force exerted on charge by long wire
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
?= h/v(2mE)
µ=s^2
F = µ0 q v I / 2pr

39. Complex impedance (expressions for capacitor and inductor)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
qvb = mv²/R
Z_c = -i/(?C) ; Z_L = i ? L

40. Heat added
NC?T
4H + 2e- ? He +2? + 6?
Const: 2t = (n +.5)? Destructive 2t = n?
<T> = 1/2 * <dV/dx>

41. Lab: Standard Deviation of Poisson
v(mean)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
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
T^2 = k R^3 - k=constant

42. Solid: Resistivity of Semi-Conductor
?~1/T
<T> = -<V>/2
S = k ln[O] ; dS = dQ/T
Exponentially decreasing radial function

43. Charge in Capacitor
Always Real
?_max = b/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)
Q = CVexp(-t/RC)

44. Biot-Savart law
T = I?²/2
L = mr²d?/dt
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
(° of Freedom)kT/2

45. Perpendicular axis theorem
F = µ0 q v I / 2pr
? = 1.22?/D
ds² = (c*dt)² - ?(x_i)²
I_z = I_x + I_y (think hoop symmetry)

46. Gibbs Factor
Exp(N(µ-e)/t)
L = L_0 Sqrt[1-v^2/c^2]
I = I_0 Cos[?]^2
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

47. Rocket Equation
Dv = -udm/m - v = v0 + u ln(m0/m)
P +1/2 ? v² + ?gh = Constant
Faraday/Lenz: current inducted opposes the changing field
ma + kx = 0

48. Energy in Inductor
V(r) + L²2/2mr²
.5 LI²
L = mr²d?/dt
Measurements close to mean

49. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
N d flux / dt
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
ma + kx = 0
Measurements close to true value

50. Induced EMF of solenoid
N d flux / dt
?mv
Cos[?] Sin[?] -Sin[?] Cos[?]
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])