An electron is accelerated from rest through a voltage of 600 V.The electron enters a uniform magnetic field of magnitude 5.7 * 10^-2 T and follows a circular path.Determine the radius of the circular path.

Question

Quizplus · Accepted Answer

The radius of the circular path of the electron is given by:

r = mv / (|q| B)

where m is the mass of the electron, v is its velocity, |q| is the magnitude of its charge, and B is the magnetic field strength. Since the electron is accelerated through a voltage V, it gains a kinetic energy of

K = qV

where q is the charge on the electron. Using the conservation of energy, we can equate this energy to the kinetic energy of the electron in the circular path:

K = (1/2)mv^2

Solving for the velocity, we get:

v = sqrt(2K / m)

Substituting this expression for v in the equation for r, we get:

r = sqrt(2Km) / (|q| B) = sqrt(2qVm) / (|q| B)

Now, plugging in the given values, we get:

r = sqrt(2*1.6e-19*600*9.1e-31) / (1.6e-19*5.7e-2) = 1.5e-3 m

Therefore, the correct answer is (C), 1.5 x 10^-3 m.

An Electron Is Accelerated from Rest Through a Voltage of 600