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midterm_solution_2005 - ECE120 Spring 2005 Midterm Exam...

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Unformatted text preview: ECE120, Spring, 2005 Midterm Exam Closed Book, 100 Points Name_______________________________________ 1) (5 pts) What is the principal source of the sun’s heat and light? a) Nuclear fusion b) Atomic fission c) Gravity d) Pressure 2) (5 pts) When we speak of the surface of the sun, we are referring to the a) Solar Corona b) Photosphere c) Chromosphere d) Radiative Zone 3) (5 pts) The magnetic field of the sun reverses sign (approximately) once every a) century b) 50 years c) 23 years d) 11 years 4) (5 pts) What is the approximate age of the sun? a) 4.5 thousand years b) c) 4.5 billion years d) 4.5 million years 4.5 trillion years 5) (5 pts) Sunspots are thought to be regions of a. higher magnetic field and cooler plasma (relative to surrounding regions) b. higher magnetic field and hotter plasma c. lower magnetic field and cooler plasma d. lower magnetic field and hotter plasma 6) (5 pts) Which planet has little or no atmosphere? a) Mercury b) Venus c) Earth d) Mars 7) (5 pts) Which planetary body has an atmosphere with pressure roughly 90 times that of the earth? a) Mercury b) Venus c) Moon of the Earth d) Mars 8) (5 pts) Which planetary surface most resembles the lunar surface? a) Mercury b) Venus c) Earth d) Mars 9) (5 pts) What is the location of Olympus Mon, the largest mountain in the solar system? a) Mercury b) Venus c) Moon of Earth d) Mars 10) (5 pts) Assuming that the electron density at the F-2 peak represents the maximum -3 ionospheric density, and further assuming that the density is 4 ⋅106 cm , then what is the minimum radio frequency at which communications with a satellite above the F2 layer can be established? Hint: The plasma frequency f p is approximately f p = 9 n KHz, where n is the electron number density in units of cm-3 a) c) 1 MHz 18 MHz b) d) 9 MHz 36 MHz 11) (10 pts, Answer on a separate sheet) Where is the ozone layer located, and why? Ozone is created naturally in the stratosphere by the combining of atomic oxygen (O) with molecular oxygen (O2). The altitude corresponds to the region where ultraviolet rays begin to split molecular oxygen, forming O, which then combines with the remaining O2 to produce ozone (O3). At much higher altitudes the radiation is too strong and the density of O2 to small to form ozone, while at lower altitudes, very little UV penetrate, and the density of atomic oxygen si too low. 12) (10 pts, Answer on a separate sheet) Starting with the equation of hydrostatic equilibrium (no motion of the fluid), prove that the atmospheric pressure decreases exponentially as a function of altitude. You may assume that the temperature is isothermal. Be sure to define all of your symbols. We have dP = −gρ dz When temperature is held constant, the density of a gas is proportional to pressure (an example of the ideal gas law), and we have P = ρ KT , where K is a constant. It follows that n( z ) = n0 e − zg / KT 13) (10 points, Answer on a separate sheet) Assume that you are given a particle that is trapped in the earth’s dipolar magnetic field. At the equator ( θ = π / 2 ), the radial position of the particle is LRE , where L is the L shell value, and RE is the radius of the earth. Prove that the co-latitude θ at which the particle mirrors (reflects) depends only on the particle pitch angle at the equator. Hint: assume that all electric fields are zero and that the particle magnetic moment is conserved. First, use conservation of the magnetic moment to write W⊥0 / W⊥ = B0 / B , where W⊥0 is the perpendicular particle energy at the equator, B0 is the magnetic field at the equator, W⊥ is the perpendicular particle energy at the mirror point, and B is the magnetic field at the mirror point. Since there is no parallel motion at the mirror point, we have W⊥ = W , where W is the total energy of the particle (which is constant). Thus, W⊥0 W⊥0 B = = sin 2 α 0 = 0 W⊥ W B The problem reduces to finding the variation of the magnetic field magnitude along the field line. Using B = Br2 + Bθ2 , we get 3 r L RE The radial distance r in the previous equation is the radial position at the mirror point, which can be obtained from the equation for the magnetic field line r = LRE sin 2 θ . Thus, B= µ 3 3cos 2 θ + 1 B0 = µ 3 3 B L3 RE =3 B0 r 3cos 2 θ + 1 = 3cos 2 θ + 1 sin 6 θ which finally yields B0 sin 3 θ = sin α 0 = 4 B 3cos 2 θ + 1 Thus, the co-latitude at which reflection occurs is a function only of the equatorial pitch anle of the particle. 14) (10 points, Answer on a separate sheet) Why did Biermann think cometary observations indicated the existence of a “corpuscular radiation?” Because of the existence of a second, istp.gsfc.nasa.gov/Education/wsolwind.html:) ion tail (see http://www- 15) (10 points, Answer on a separate sheet) For the Parker solar wind model, what is the radial dependence of the mass density at far distances from the sun? Hint: The solar wind velocity at far distances is approximately constant. Use ∇i ρV = () 1 d 2 d ( ρVr ) r =0 r 2 dr dr It follows that ρ= where C is a constant. Useful Equations and Definitions C r 2Vr Grad and Divergence operators in Cartesian coordinates. Assume F and A only functions of z. ∇F = dF ˆ r dr dF ˆ z dz ∇i A = dAz dz Grad and Divergence operators in Spherical coordinates. Assume F and A only functions of r. ∇F = ∇i A = 1 d 2 dAr r r 2 dr dr Fluid Equations: the continuity equation and the momentum equations are ∂ρ dV + ∇i ρV = 0 = −∇P − ρ g ρ dt ∂t ˆ Where ρ is the mass density, V is the fluid velocity and g = gz is the gravitational 2 ˆ constant for atmospheric problems, and g = GM s r / r is used for solar wind problems. () The equation for the dipolar field of the Earth is (spherical coordinates) r3 where µ is the Earth’s magnetic dipole. B=− µ ( 2rˆ cosθ + θˆ sin θ ) The equation for a dipolar magnetic field line is r = LRE sin 2 θ , where LRE is the radial position for a co-latitude of θ = π / 2 (i.e., at the equator), RE is the radius of the Earth, and L is a dimensionless length called the L shell. The particle magnetic moment is defined as W⊥ / B , where W⊥ is the particle energy perpendicular to the field. The particle pitch angle α is defined through the equation tan α = W⊥ / W , where W is defined as the parallel energy of the particle. ...
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