Question

A cosmic ray electron moves at 7.50×10^6 m/s perpendicular to the Earth’s magnetic field at an altitude where the field strength is 1.00×10^−5 T. What is the radius of the circular path the electron follows?

a) 3.75 m
b) 5.00 m
c) 6.67 m
d) 9.00 m

Answer 1

To find the radius of the circular path the electron follows, we can use the formula for the magnetic force on a charged particle moving in a magnetic field. By equating this force with the centripetal force, we can solve for the radius.

Step-by-step explanation:

To find the radius of the circular path the electron follows, we can use the formula for the magnetic force on a charged particle moving in a magnetic field. The force is given by the equation F = qvB, where F is the force, q is the charge of the particle, v is the velocity of the particle, and B is the magnetic field strength. In this case, the force is provided by the centripetal force, which is given by the equation F = mv^2/r, where m is the mass of the particle and r is the radius of the circular path. By equating these two forces, we can solve for the radius.

First, let's find the charge of the electron. The charge of an electron is -1.6 x 10^-19 Coulombs. Now, let's find the mass of an electron. The mass of an electron is 9.11 x 10^-31 kilograms.

Using these values, we can set up the following equation: qvB = (mv^2)/r. Plugging in the given values, we get (-1.6 x 10^-19 C)(7.5 x 10^6 m/s)(1.00 x 10^-5 T) = (9.11 x 10^-31 kg)(7.5 x 10^6 m/s)^2/r.

Simplifying the equation, we get -1.2 x 10^-12 = (9.11 x 10^-31)(5.63 x 10^13)/r. Solving for r, we find that the radius of the circular path the electron follows is approximately 6.67 meters. Therefore, the correct answer is option c) 6.67 m.