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Assumed that the Earth's magnetic field is approximated by a dipole field and charged particles mirror at the surface of the Earth, calculate the equatorial loss cone at L = 6. 2. Define the differential flux tube volume V, the number of particles N, and the specific entropy as: V = 1 %, N = still , and H = spiral B, n, and p denote magnetic field strength, particle number density, and pressure, respectively. y is the adiabatic index. The integral is taken over the full length of a flux tube with a small cross section. In ideal MHD convection, these quantities are conserved. A) Pinpoint the detailed assumptions of "ideal MHD convection", B) With the ideal MHD assumption, prove that V, N, and Hare conserved. а 3. [Problem 6.6 in Kivelson, M. G., & Russell, C.T. (1995). Introduction to space physics) A) If the polar cap is defined by the open field lines that enter the taillobe, and if it can be approximated by a circle or radius 15" centered on the magnetic dipole axis, how much flux is there in a lobe of the geomagnetic tail? B) If none of this flux crosses the neutral or current sheet in the tail, if no solar wind plasma enters the tail field lines, and if the strength of the interplanetary magnetic field is 6 nT and B-1, what is the radius of the distant taillobe? 4. Discuss the similarities and differences of convection between the Earth and Jupiter. (Sketch and describe the Dungey and Vasyliunas cycle from both the magnetospheric and ionospheric point of views, Illustrating the key properties e.g. plasma flow, electric field, and currents etc Quantitative descriptions will be appreciated.)