NASA\'s Juno spacecraft recently entered into an orbit around Jupiter. See the 2

Question

NASA's Juno spacecraft recently entered into an orbit around Jupiter. See the 2 attached graph, which displays levels of detected radiation emitted by the planet as a function of wavelength, and read the text below the graph of this assignment). If you need a clearer graph, use the link. Some of the radiation emitted by the planet can be associated with the fact that charged particles executing circular and helical orbits in magnetic fields will emit electromagnetic radiation at their orbital frequency (cyclotron frequency 0. Electromagnetic w at the speed of light, c 3.0 x 108 m/s, and their frequency (f is related to their wavelength (n) by the equation: c Please look at the graph, read the accompanying text and carefully read the text above before you ask questions. can use the theory of circularand helical charged particle motions in magnetic fields that we have been discussing in class to explain part of the observed spectrum. Approximately what wavelength range is that? How do you know? Sketch the graph (roughly on your solution sheet and mark the data range that corresponds to the range in question. Does radiation generated by these motions appear to dominate the spectrum, or are there other sources that are more significant? If so, what are those sources and how do you know? b) Based on this radiation pattern determine the upper and lower bounds on the magnitude of the planet's magnetic field. Briefly explain the logic behind your calculations (not the algebra, which explains itself c) Consider the helical motion of an electron in the region that corresponds to the weakest magnetic field found in part b. The helix has a pitch of 2 cm and a radius of 0.9 cm. Determine the parallel and perpendicular components of the electron's velocity, its speed and the angle its velocity vector makes with the magnetic field direction 3) The space between two charged metal plates is filled with a uniform electric field as shown below. A beam of ions enters the device as shown. The plates are part of a velocity selector used to allow only those particles, from the ion beam, that enter the device with a specific velocity to pass through undeflected. A uniform magnetic field is also needed ion beam undefected particles a) Assume that the ions are positively charged. In which direction does the magnetic field

Explanation / Answer

2) As the decimetric radiation given is due to the charged particles in the magentic fields,

Wave length = 3cm to 3m

We can estimate the magnetic strength of Jupiter by

The equation, qvB = mrw^2

And B = m*w/q

w = 2*pi*f = 2*pi*c/lambda

So B =2* pi*c* /(q*lambda)

So uooer bound B (max) = 2* pi*c* /(q*lambda (min) ) which is at 3 cm wave length

and lower bound is at 3 m wavelength

c) pitch = 2cm

Time taken for 1 revolution = 2*pi/ w

where w = Angular frequency = 2*pi* c/ lambda. So Time = lambda / c

Velocity along the axis of helix = Pitch / Time for 1 revolution

3) Velocity selector For undeflected particle, Net force = Zero.

So q*v* B = q* E

So v = E/B

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