A magnetic field of density (B) of 20μT is applied normally to a proton moving at a speed of 30,000 km/s causing it to rotate in a circular path as shown in the following diagram. Calculate the oscillation frequency.(proton charge = 1.6x10-19 C, proton mass = 1.67×10-27 kg)Select one:a. None of the choicesb. 152.6 Hzc. 305.1 Hz d. 457.7 Hze. 55.4 Hz
Question
A magnetic field of density (B) of 20μT is applied normally to a proton moving at a speed of 30,000 km/s causing it to rotate in a circular path as shown in the following diagram. Calculate the oscillation frequency.(proton charge = 1.6x10-19 C, proton mass = 1.67×10-27 kg)Select one:a. None of the choicesb. 152.6 Hzc. 305.1 Hz d. 457.7 Hze. 55.4 Hz
Solution
To solve this problem, we need to use the formula for the cyclotron frequency (also known as the gyrofrequency), which is given by:
f = qB / (2πm)
where: f is the frequency, q is the charge of the proton, B is the magnetic field density, and m is the mass of the proton.
Substituting the given values:
f = (1.6x10^-19 C * 20x10^-6 T) / (2π * 1.67x10^-27 kg)
Solving this equation gives us:
f ≈ 305.1 Hz
So, the correct answer is c. 305.1 Hz.
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