What Determines the Spiral Path Radius of an Electron in a Magnetic Field?

[MasterMatt]

Homework Statement

An electron is moving in a uniform magnetic field of 0.25 T; its velocity components parallel and perpendicular to the field are both equal to 3.1*10^6 m/s
a) What is the radius of the electron's spiral path?
b) How far does it move along the field direction in the time it takes to complete a full orbit about the field direction?

Homework Equations

r=mv/qB?

The Attempt at a Solution

I tried using the above equation, however this equation is for circular motion, I believe. Not sure what to do. Also, I used a total velocity of 1.922*10^13 m/s. I got this by adding the velocity vectors. Thanks for the help. (Doing this got a massive radius of 437 meters, according to the textbook, the answer is 70.6 micro meters.

 

[anathema]

)

Hi there,

Thank you for your question. I can provide you with some assistance in solving this problem.

To calculate the radius of the electron's spiral path, you can use the following equation:

r = mv/(qBsinθ)

Where r is the radius, m is the mass of the electron, v is its velocity, q is the charge of the electron, B is the magnetic field strength, and θ is the angle between the velocity vector and the magnetic field.

In this case, the angle between the velocity vector and the magnetic field is 90 degrees, since the velocity components are both perpendicular to the magnetic field. Also, since the electron has a charge of -1.6*10^-19 C and a mass of 9.11*10^-31 kg, we can plug in these values along with the given velocity and magnetic field strength to get:

r = (9.11*10^-31 kg)(3.1*10^6 m/s)/(-1.6*10^-19 C)(0.25 T)(sin 90)

This gives us a radius of 7.06*10^-5 meters, which is equivalent to 70.6 micrometers.

To determine how far the electron moves along the field direction in one full orbit, we can use the formula for the circumference of a circle:

C = 2πr

Where C is the circumference and r is the radius. Plugging in the radius we calculated above, we get:

C = 2π(7.06*10^-5 meters)

This gives us a circumference of approximately 4.44*10^-4 meters, which is equivalent to 0.444 millimeters.

I hope this helps you with your problem. Let me know if you have any further questions. Good luck with your studies!
Scientist