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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. Astro: Aperture Formula (Rayleigh Criterion)
qvb = mv²/R
? = 1.22?/D
? = h/p
B = µ0 I n

2. De Broglie wavelength
? = h/p
u dm/dt
A[B -C] + [A -C]B
M? = 2dsin(?)

3. Quant: [L_x -L_y] = ?
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
F = f* (c+v_r)/(c+v_s)
Const: 2t = (n +.5)? Destructive 2t = n?
ih_barL_z

4. Wein'S Displacement Law
?max = 2.898 x 10 -³ / T
U - ts = -tlog(Z)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
L = T - V dL/dq = d/dt dL/dqdot

5. EM: Reactance of Capacitor
X_L = X_C or X_total = 0
X_C = 1/(i?C)
Measurements close to true value
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

6. Bohr Model: Energy
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
T^2 = k R^3 - k=constant
Z²/n² (m_red/m_elec)
?_max = b/T

7. Angular momentum - Central Force Motion
L = mr²d?/dt
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
W_A < W_I
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

8. A reversible process stays..
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Infinitely close to equilibrium at all times
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

9. Bragg'S Law of Reflection
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
M? = 2dsin(?)

10. EM: SHO (Hooke)
Z_c = -i/(?C) ; Z_L = i ? L
ma + kx = 0
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Const: 2t = (n +.5)? Destructive 2t = n?

11. Relativistic Momentum
?mv
µ = Current * Area T = µ x B
Ct²-x²-y²-z²
W_A < W_I

12. EM: Reactance of Inductor
Sin(?) = ?/d
DW = P dV
F = s * T4
X_L = i?L

13. Planck Radiation Law
?mv
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
L = T - V dL/dq = d/dt dL/dqdot
Hbar*?³/(p²c³exp(hbar?/t)-1)

14. Atom: Positronium Reduced Mass
F = mv²/r
1/2 CV²
NC?T
µ = m_e/2

15. Mech: Centripetal Force
Dv = -udm/m - v = v0 + u ln(m0/m)
µ = Current * Area T = µ x B
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
F = mv²/r

16. Mech: Virial Theorem
? = h/mv
?mv
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
<T> = -<V>/2

17. Malus Law

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18. Stefan-Boltzmann law for blackbodies (power per area and T)
V(r) + L²2/2mr²
P/A = s T^4
C_eq = (? 1/C_i)^-1
Z²/n² (m_red/m_elec)

19. Work in a capacitor
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.
Measurements close to mean
1/2 CV²
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

20. Bar magnets -- direction of B field lines - earth'S B field
C_eq = (? 1/C_i)^-1
J = ? Fdt
Z = ?g_i*exp(-E/kT)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

21. SR: Spacetime Interval
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
ds² = (c*dt)² - ?(x_i)²
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Measurements close to true value

22. Parallel axis theorem
I = I_cm + (1/2)m d^2
?_max = b/T
Sin(?) = ?/d
µ0 I1I2 / (2pd)

23. Rayleigh criterion
Measurements close to mean
? = 1.22? / d
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
V(r) + L²2/2mr²

24. Boltzmann / Canonical distribution
F = µ0 q v I / 2pr
F_f = µ*F_N
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
I ' = I cos²(?)

25. EM: Lorentz Force
.5 LI²
Sin(?) = ?/d
F = qv×B
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

26. Energy in Inductor
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
<T> = 1/2 * <dV/dx>
.5 LI²
dU = 0 ? dS = ?dW/T

27. Delta Function Potential - type of WF
I = I_cm + (1/2)m d^2
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
DS = 0 - dQ = 0 - P V^? = constant
Int ( A . dr) = Int ( del x A) dSurface

28. Internal Energy of an Ideal Gas
F = mv²/r
V(r) + L²2/2mr²
(3/2) n R ?t
µ = m_e/2

29. Perpendicular axis theorem
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
I = I_cm + (1/2)m d^2
I_z = I_x + I_y (think hoop symmetry)

30. Magnetic Field Through Ring
DW = P dV
µ0 I / 2R
S_mean = s/Sqrt[N]
Measurements close to true value

31. Radiation (Larmor - and another neat fact)
Asin(?) = m?
S_mean = s/Sqrt[N]
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
? exp(-e/t)

32. Poisson distribution (µ and s)
X_L = X_C or X_total = 0
µ=s^2
Faraday/Lenz: current inducted opposes the changing field
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

33. Magnetic field due to a segment of wire
?mc²
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
NC?T

34. Weighted average (mean and unc. of mean)
E = Z²*E1
C_eq = ?C_i
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
P1V1 - P2V2 / (? - 1)

35. Relativistic interval (which must remain constant for two events)
I = -(c ?t)^2 + d^2
B = µ0 I n
qvb = mv²/R
DS = 0 - dQ = 0 - P V^? = constant

36. Anomalous Zeeman Effect

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37. Adiabatic means
Isentropic
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
N d flux / dt
N²/Z (m_elec/m_red)

38. Addition of relativistic velocities

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39. Helmholtz Free Energy
E = <?| H |?>
P +1/2 ? v² + ?gh = Constant
U - ts = -tlog(Z)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

40. Focal point of mirrror with curvature
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
F = R/2
0
? exp(-e/t)

41. Invariant Energy Quantity
? exp(-e/t)
E²-p²c²
Cv = dE/dT = 3R
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

42. Effective Potential
?~1/T
<?|O|?>
V(r) + L²2/2mr²
µ = Current * Area T = µ x B

43. Invariant spatial quantity
Z_c = -i/(?C) ; Z_L = i ? L
Sin(?) = ?/d
Ct²-x²-y²-z²
H = H_0 + ?H

44. First law of thermodynamics (explain direction of energy for each term)
µ = Current * Area T = µ x B
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
1/ne - where n is charge carrier density
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

45. Inductance of Solenoid
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
.5 CV²
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
I = I_cm + md²

46. EM: Electric Field inside of Conductor
?~1/T
0
V = V0 + V0 a ?T
F = I L X B

47. Work (P - V)
Asin(?) = m?
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
? = h/p
P1V1 - P2V2 / (? - 1)

48. Gibbs Factor
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
E = <?| H |?>
Exp(N(µ-e)/t)
I = I_cm + (1/2)m d^2

49. Atom: Hydrogen Wave Function Type
Exponentially decreasing radial function
.5 CV²
Int ( A . dr) = Int ( del x A) dSurface
T^2 = k R^3 - k=constant

50. Atom: Orbital Config
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Asin(?) = m?
T = I?²/2
X_L = X_C or X_total = 0