only do parts f & g **Magnetic Fields and Electrons in Sunspots**Consider an electron gyrating in the magnetic field associated with a sunspot with a magnetic field strength of 0.25 T.**a) Cyclotron Frequency**- Compute the cyclotron frequency \(\omega_c\) of the electron in Hertz.**b) Electron Velocity from Temperature**- 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: \[ v = \sqrt{\frac{3k_BT}{m}} \] Compute the velocity of the electron in meters per second. - \(k_B\) is Boltzmann’s constant \((1.38 \times 10^{-23} \, \text{J/K})\).**c) Larmor Radius**- Calculate the Larmor radius \(r_L\) of gyration of the electron.- Compute and interpret the ratio of this radius to the radius of the Sun \((6.96 \times 10^8 \, \text{m})\).**d) Centripetal Acceleration**- Calculate the centripetal acceleration \(a\) in \(\text{m/s}^2\) of the electron as it gyrates along the magnetic field lines associated with the sunspot.**e) Power Emitted by the Electron**- Calculate the power \(P\) in Watts emitted by this electron as it gyrates along the magnetic field lines associated with the sunspot.**f) Proton Calculations**- Repeat parts (a) through (e) for a proton.**g) Ratio of Power Emissions**- Compute the ratio of the power emitted by the electron to the power emitted by the proton.- Analyze if the cyclotron emission detected from the Sun is dominated by emission from electrons or protons. Explain your answer.

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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 wc 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, 3KBT v = m to compute the velocity of the electron in meters per second. Here, kB is Boltzmann's constant (1.38 x10-23 J/K). c) Calculate the Larmor radius rL of gyration of the electron. Compute and physically interpret the ratio of this radius to the radius of the Sun (6.96×10³ m). 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. f) Repeat Parts (a) through (e) for a proton.

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 wc 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, 3KBT v = m to compute the velocity of the electron in meters per second. Here, kB is Boltzmann's constant (1.38 x10-23 J/K). c) Calculate the Larmor radius rL of gyration of the electron. Compute and physically interpret the ratio of this radius to the radius of the Sun (6.96×10³ m). 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. f) Repeat Parts (a) through (e) for a proton.