Assume a coordinate system where the vertical is the positive z direction, x is toward the Sun and y completes the right hand system and points to the west. In the center of the magnetotail, at x = -30Re, y=0, z=0, there is an electric field pointing in the y-direction (east-west direction) caused by the solar wind.
(a) Calculate the magnetic field strength at x=-30Re.
(b) Find the direction of the magnetic field at the same position. Which way is it pointing? Make a sketch in the xz-plane and show the direction of magnetic field at x=-30 Re and z=0.
(c) Using the magnetic field and electric field, determine the direction of the particle motion. Which direction do they move? Show your answer on a sketch.
(d) Make a sketch of the magnetosphere in xy-plane and show direction of magnetic field, electric field and the particle motion in this plane.
(e) What would be the speed of the particles in the plasma sheet if the electric field is 1 mV/m and magnetic field is 5nT.
(f) Calculate the radius of an electron and an ion in the solar wind moving with a speed of 400 [km/sec] and temperature of 10^5 [K]; in the plasma sheet of magnetosphere with a temperature of 10^6 [K] and speed of about 50 [km/sec]; and in the ionosphere where the ion and electron temperatures are 2500 [K] and both species move with thermal velocity. Assume that the total magnetic field in the solar wind is 10 [nT] while it is 50 [nT] in the plasma sheet and 500 [nT] in the ionosphere. Make a Table that shows your calculations for comparisons. This is to give you a sense how the gyroradius for an electron and ion differs in different environments.