Question

The aurora is caused when electrons and protons, moving in the Earth's magnetic field of 5.0 x 10⁻⁵ T, collide with molecules of the atmosphere and cause them to glow.

What is the radius of the circular orbit for an electron with speed 4.0 x 10⁶ m/s? Assume that the electron moves in a plane perpendicular to the magnetic field. Express your answer with the appropriate units.

Answer 1

The radius of the circular orbit for an electron with speed 4.0 x 10⁶ m/s is 5.0 x 10⁶ m.

Step-by-step explanation:

The radius of the circular orbit for an electron with speed 4.0 x 10⁶ m/s can be calculated using the equation for the centripetal force:

F = |qV|B = |eV|B

where 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 charge of an electron is e = -1.6 x 10⁻¹⁹ C. We can rearrange the equation to solve for the radius of the orbit:

r = mv / (eB) = (4.0 x 10⁶ m/s)/(1.6 x 10⁻¹⁹ C)(5.0 x 10⁻⁵ T) = 5.0 x 10⁶ m

Therefore, the radius of the circular orbit for an electron with speed 4.0 x 10⁶ m/s is 5.0 x 10⁶ m.