a) Compute the gyroradius r in meters of the oxygen ion just as it leaves Io. b) Compute the centripetal acceleration a in meters per second-squared experienced by the oxygen ion as it gyrates in its gyroradius. =) Compute the power P radiated in Watts by the ion.
a) Compute the gyroradius r in meters of the oxygen ion just as it leaves Io. b) Compute the centripetal acceleration a in meters per second-squared experienced by the oxygen ion as it gyrates in its gyroradius. =) Compute the power P radiated in Watts by the ion.
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Transcribed Image Text:Jupiter's powerful magnetic field interacts very strongly with its innermost major moon Io.
Volcanoes on Io eject large amounts of molecules of sulfur dioxide into space: ultraviolet
radiation from the Sun photodissociates these molecules into ions of atomic sulfur and
oxygen. Consider an ion of oxygen that escapes from Io: the charge of this ion is q=1.28
x 10-18 C, the mass of this ion is m = 2.67× 10-26 kg and its initial velocity when it is ejected
is v =
50 km/s. Assume that the strength of Jupiter's magnetic field at the radius of Io's
orbit is Bo = 10-6 T (note that Io's orbital plane corresponds roughly to Jupiter's equatorial
plane, so that the ion begins its journey in Jupiter's equatorial plane) and that the strength of
Jupiter's magnetic field at its poles is BM
field strength attains its maximum value).
q=1.28 x 10-18 C Bo
т — 2.67x 10-26
v = 50 km/s
= 5000 x 10-6 T (this is where Jupiter's magnetic
10-6 T
= 5000 x 10-6 T
Вм
a) Compute the gyroradius r in meters of the oxygen ion just as it leaves Io.
b) Compute the centripetal acceleration a in meters per second-squared experienced by the
oxygen ion as it gyrates in its gyroradius.
c) Compute the power P radiated in Watts by the ion.
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