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Magnetic force help

  • Thread starter Gunman
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Homework Statement


An electron moves in a circular path in a vacuum under the influence of a magnetic field perpendicular to and into the paper.If there is another electron which moves with a higher speed in a circular path in the same B-field, state and explain how each of the following will be affected as compared to the first electron?
(c) The radius of the circular path


Homework Equations


F = Bqv
B = flux density
q = charge
v = velocity of the charge


The Attempt at a Solution



F(m) = Bqv
Since F(m) causes the centripetal acceleration of electron
F(m) = Bqv = mv^2/r
r = mv/Bq
Therefore it can be concluded that r increases as v increases?

But how can this be case as,
F(m) = Bqv, and F(m) increases as velocity of the charge increases
If F(m) increases, r would decrease as it is inversely proportional to F
in the equation F(m) = mv^2/r.

So would r increase or decrease if a faster electron moves in a circular path in a vacum under the influence of a magnetic field perpendicular to and into the paper.
 

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  • #2
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
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6

Homework Statement


An electron moves in a circular path in a vacuum under the influence of a magnetic field perpendicular to and into the paper.If there is another electron which moves with a higher speed in a circular path in the same B-field, state and explain how each of the following will be affected as compared to the first electron?
(c) The radius of the circular path


Homework Equations


F = Bqv
B = flux density
q = charge
v = velocity of the charge


The Attempt at a Solution



F(m) = Bqv
Since F(m) causes the centripetal acceleration of electron
F(m) = Bqv = mv^2/r
r = mv/Bq
Therefore it can be concluded that r increases as v increases?

But how can this be case as,
F(m) = Bqv, and F(m) increases as velocity of the charge increases
If F(m) increases, r would decrease as it is inversely proportional to F
in the equation F(m) = mv^2/r.

So would r increase or decrease if a faster electron moves in a circular path in a vacum under the influence of a magnetic field perpendicular to and into the paper.
You have clearly put a lot of thought into this question, perhaps a little too much :wink:. Consider your final equation,

[tex]F = \frac{mv^2}{r}[/tex]

And your final comment,
If F(m) increases, r would decrease as it is inversely proportional to F
You are correct that the magnetic force increases, but you forget that the speed v has also increased. Notice that the speed is raised to the second power and therefore will have a much greater effect on the magnetic force that the radius since the radius is only raised to the fist power.
 

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