Electron with circular trajectory in a magnetic field

[merdeka]

Homework Statement

An electron, animated by a speed $\vec{v}$ penetrates a uniform magnetic field $\vec{B}$ . The vectors $\vec{v}$ and $\vec{B}$ are orthogonal, the trajectory of the particle is a circle of radius $R$.

Calculate the module $\vec{v}$ of the electron's velocity.

me = 9,109 382 15 × 10−31 kg
q = 1,602 176 53 × 10−19 C
B = 1,0 T
R = 1,0 cm

Relevant Equations

$F=q\cdot v\cdot B\cdot\cos(\vec{v},\vec{B})$

I'm not sure how I'm able to calculate the velocity of the particle using the formula without knowing the force exerted on it. Also, I don't understand why the question also provides the mass of the electron.

 

[berkeman]

Just use the Lorentz force equation and combine it with the centripetal force equation for uniform circular motion of a mass.

As for the mass of the electron, it may end up cancelling out when you combine those two equations, but I don't know for sure without working the problem.

Please show us those two equations and how you combine them to work toward the solution. Thanks.

 

[merdeka]

I don't understand how the Lorentz force must equal the centrifugal force. I know that their vectors are both orthogonal to $\vec{v}$ and $\vec{B}$

 

[PeroK]

I don't understand how the Lorentz force must equal the centrifugal force. I know that their vectors are both orthogonal to $\vec{v}$ and $\vec{B}$

The Lorentz force IS the centripetal force. There is only one force here.

The key is that the magnetic force is always perpendicular to the velocity. And, if the magnetic force is constant, then this implies circular motion.