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d) Calculate the centripetal acceleration a in m/s² of the electron as it gyrates along the magnetic field lines associated with the sunspot. e) Calculate the power P in Watts emitted by this electron as it gyrates along the magnetic field lines associated with the sunspot.

d) Calculate the centripetal acceleration a in m/s² of the electron as it gyrates along the magnetic field lines associated with the sunspot. e) Calculate the power P in Watts emitted by this electron as it gyrates along the magnetic field lines associated with the sunspot.

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Only do parts d & e

Consider an electron gyrating in the magnetic field associated with a sunspot which has a magnetic field strength of 0.25 T. a) Compute the cyclotron frequency \( \omega_c \) of the electron in Hertz. b) The typical temperature of a sunspot is 3500 K. Use this temperature and the equipartition equation for velocity \( v \), temperature \( T \), and mass \( m \) of a particle, that is, \[ v = \sqrt{\frac{3k_BT}{m}}, \] to compute the velocity of the electron in meters per second. Here, \( k_B \) is Boltzmann’s constant (1.38 × 10\(^{-23}\) J/K). c) Calculate the Larmor radius \( r_L \) of gyration of the electron. Compute and physically interpret the ratio of this radius to the radius of the Sun (6.96×10\(^8\) m). d) Calculate the centripetal acceleration \( a \) in m/s\(^2\) of the electron as it gyrates along the magnetic field lines associated with the sunspot. e) Calculate the power \( P \) in Watts emitted by this electron as it gyrates along the magnetic field lines associated with the sunspot. f) Repeat Parts (a) through (e) for a proton. g) Compute the ratio of the power emitted by the electron to the power emitted by the proton. Therefore, is the cyclotron emission detected from the Sun dominated by emission from electrons or protons? Explain your answer.
Transcribed Image Text:Consider an electron gyrating in the magnetic field associated with a sunspot which has a magnetic field strength of 0.25 T. a) Compute the cyclotron frequency \( \omega_c \) of the electron in Hertz. b) The typical temperature of a sunspot is 3500 K. Use this temperature and the equipartition equation for velocity \( v \), temperature \( T \), and mass \( m \) of a particle, that is, \[ v = \sqrt{\frac{3k_BT}{m}}, \] to compute the velocity of the electron in meters per second. Here, \( k_B \) is Boltzmann’s constant (1.38 × 10\(^{-23}\) J/K). c) Calculate the Larmor radius \( r_L \) of gyration of the electron. Compute and physically interpret the ratio of this radius to the radius of the Sun (6.96×10\(^8\) m). d) Calculate the centripetal acceleration \( a \) in m/s\(^2\) of the electron as it gyrates along the magnetic field lines associated with the sunspot. e) Calculate the power \( P \) in Watts emitted by this electron as it gyrates along the magnetic field lines associated with the sunspot. f) Repeat Parts (a) through (e) for a proton. g) Compute the ratio of the power emitted by the electron to the power emitted by the proton. Therefore, is the cyclotron emission detected from the Sun dominated by emission from electrons or protons? Explain your answer.
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