An electron enters a magnetic field

AI Thread Summary
The discussion centers on solving a physics problem involving an electron entering a magnetic field. The original poster (OP) attempts to relate kinetic energy and centripetal force to derive equations for the radius of the electron's path. Responses indicate that the OP's approach is generally correct, but suggest showing more detailed workings to identify potential mistakes. Additionally, it is noted that finding velocity is unnecessary for the second part of the problem, as kinetic energy can be directly related to force and radius. Overall, the conversation emphasizes clarity in problem-solving steps and the relationships between physical concepts.
Dominic90
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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?
 
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Title: “An electron enters a magnetic field”

Ah, I was expecting a joke.
 
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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.
 
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Steve4Physics said:
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.
 
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@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.
 
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Steve4Physics said:
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
 
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