An aurora (ie, the Northern Lights) is produced when charged particles are eject

Question

An aurora (ie, the Northern Lights) is produced when charged particles are ejected from the Sun and travel towards the Earth, where they spiral through the Earth%u2019s magnetic field, radiating light as the Earth%u2019s magnetic field causes them to accelerate.

(a) Suppose that an electron from the Sun has entered Earth%u2019s magnetic field in a direction exactly perpendicular to the field lines, as

shown. In what direction (-x, +y, -z, etc) will the electron be pushed at the moment that it enters the field?

(b) Suppose that, upon entering Earth%u2019s magnetic field, the electron has been accelerated at a rate of 3.8x1012 m/s2. The strength of Earth%u2019s magnetic field at the electron%u2019s latitude is 45 %u03BCT. At what speed did the electron enter the Earth%u2019s magnetic field?

(c) The deflection of the electron induces a change in the direction of the magnetic force, resulting in a continuing series of deflections. The net result is that the electron spirals around the magnetic field lines (ie, cyclotron motion). What is the radius of the electron%u2019s

cyclotron orbit?

Explanation / Answer

a) - z direction

b)ma = qvB

==> 9.1*10^-31*3.8x10^12 = 1.6*10^-19*v*45*10^-6

==>v = 9.1*3.8*10^6/(1.6*45) = 0.48 *10^6 m/s

c)r = mv/qB = (9.1*10^-31*0.48*10^6)/(1.6*10^-19*45*10^-6) = 0.060 m

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