Radius of Circular Path Affected by Magnetic Force: Increase or Decrease?

[Gunman]

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 vacuum under the influence of a magnetic field perpendicular to and into the paper.

 

[Hootenanny]

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 vacuum 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 . Consider your final equation,

$$F = \frac{mv^2}{r}$$

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.