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,

[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.

 

[Moetasim]

The radius of the circular path will decrease as the speed of the electron increases. This is because the magnetic force (F=mBqv) is directly proportional to the velocity of the charge. As the velocity increases, the force also increases, causing the electron to move in a tighter, smaller circle. This is similar to how a car makes a tighter turn when it is going at a higher speed.

Furthermore, the radius is also inversely proportional to the magnetic field strength (B). As the B-field remains constant, an increase in velocity will result in a decrease in the radius.

In conclusion, if a faster electron moves in a circular path in a vacuum under the influence of a magnetic field, the radius of the circular path will decrease compared to the first electron. This is due to the direct relationship between velocity and magnetic force, and the inverse relationship between radius and magnetic field strength.