An electron enters a magnetic field

[Dominic90]

Homework Statement

An electron, accelerated from rest by a potential difference ∆V, enters a magnetic field B, perpendicular to the lines of force. The electron therefore travels a circular trajectory of radius r. If ∆V is doubled and B halved, what will be the radius R, as a function of r, of the new trajectory?

The same electron is now in uniform circular motion of radius 26.1 𝜇𝑚 subject to a field uniform magnetic. The magnetic force acting on it has an intensity of 1.60 ∙ 10^(−17)𝑁.

Calculate the kinetic energy of the electron.

Relevant Equations

K = (1/2) mv²
E = q ∆V
r = m v / (|q|B)
F = |q|vB
Centripetal force = mv²/r

Hi, I tried to solve this exercise but I'm not sure about the process.

First of all, I imposed that "K = E":

so that "v = √ ( (2q ∆V)/m))"

then I replaced in "r = m v / (| q |B)", v with "√ ( (2q ∆V)/m))", and found out that R = (2√(2)) r.

Then for the second point,

I imposed Lorenz Force Law = Centripetal force and isolated v.

Then I substituted v in K
and obtained that "K= (1/2 ) F r".

Is this correct?

 

[Steve4Physics]

Title: “An electron enters a magnetic field”

Ah, I was expecting a joke.

 

[hutchphd]

+
Except the joke would have to start something like "an electron, a neutrino, and a muon enter a magnetic Field..."
By the way the OP looks good to me.

 

[haruspex]

Title: “An electron enters a magnetic field”

Ah, I was expecting a joke.

... then charged out again. It wasn't very attractive and kept giving it the runaround.

 

[Steve4Physics]

@Dominic90, I also agree with your answers. (And sorry about Post #2.)

As a general point, maybe it helps to show the working, rather than just describe the 'process'. (This makes it easier to identify the source of mistakes, if there are any.)

For the second question, there is no need find v first. Note that K = ½mv² and F = mv²/r. You can easily combine these to show that K = ½Fr.

 

[Dominic90]

Title: “An electron enters a magnetic field”

Ah, I was expecting a joke.

I was expecting something about grammar since this isn't my first language, but then I cracked up xD