An electron in a magnetic field has a cyclotron frequency of 8.0 × 10¹² Hz. What is the magnetic field strength? (The mass of an electron is 9.1 × 10^-31 kg, and the charge of an electron is 1.6 × 10^-19 C.)

Question

Quizplus · Accepted Answer

The cyclotron frequency is given by:$$f_c = \frac{qB}{2\pi m}$$where:* $$f_c$$ is the cyclotron frequency* $$q$$ is the charge of the electron* $$B$$ is the magnetic field strength* $$m$$ is the mass of the electronSolving for $$B$$, we get:$$B = \frac{2\pi m f_c}{q}$$Plugging in the given values, we get:$$B = \frac{2\pi (9.1 	imes 10^{-31} 	ext{ kg})(8.0 	imes 10^{12} 	ext{ Hz})}{1.6 	imes 10^{-19} 	ext{ C}} = 0.22 	ext{ T}$$Therefore, the correct answer is C) 0.22 T.

An Electron in a Magnetic Field Has a Cyclotron Frequency