The Impact of Current on Circular Paths: Examining Equation 1

[Eddie10]

Homework Statement

Once a circular path has been obtain for the electrons, how will increasing current to the coils affect that path? Use equation 1 and the fact that e/m is a constant for the electron.

Homework Equations

e/m = 2V/B^2r^2

The Attempt at a Solution

I'm unclear as to how to find a solution because I think that the circular path of electrons will grow brighter, or grow dimmer when more current, or less current is applied, once the electrons are in a circular path.

However, how can I use the given equation to prove this?

Note, I have not conducted any type of measurements or observations of any kind, as this is a pre-lab questionnaire that I am fulfilling to get credit.

UPDATE: I firmly believe that increasing the current to the coils will make the circle larger, once the circular path has been established prior to increasing said current.

However, how can I use the given equation to show this?

As an aside, increasing the magnetic field will make the circle smaller.

 

[haruspex]

Maybe I'm misguessing the set up, but I would have thought the coils in question were generating the magnetic field, so the last line of your post seems the relevant one.

 

[Eddie10]

Maybe I'm misguessing the set up, but I would have thought the coils in question were generating the magnetic field, so the last line of your post seems the relevant one.

The set-up is going to be the traditional set-up used for the e/m experiment that is used at most universities.
The coils will generate a magnetic field, but what will increasing the current do to the circle once it is established?

I think the increased current will expand the circle and make it bigger, but I am unsure how to show this with my equation.

 

[haruspex]

The set-up is going to be the traditional set-up used for the e/m experiment that is used at most universities.
The coils will generate a magnetic field, but what will increasing the current do to the circle once it is established?

I think the increased current will expand the circle and make it bigger, but I am unsure how to show this with my equation.

If the function of the coils is to generate a magnetic field, then increasing the current will increase the field, yes? And as you wrote, increasing the field will shrink the circle.

 

[HalfLostAndSearching]

As a scientist, it is important to use mathematical equations to support our observations and predictions. In this case, we can use equation 1 (e/m = 2V/B^2r^2) to understand the relationship between current and the circular path of electrons.

First, let's break down the equation. "e/m" represents the charge-to-mass ratio of the electron, which is a constant value. "V" represents the voltage applied to the coils, "B" represents the strength of the magnetic field, and "r" represents the radius of the circular path.

From this equation, we can see that increasing the current (represented by "V") will have an inverse relationship with the radius of the circular path (represented by "r"). This means that as the current increases, the radius of the circular path will decrease. This is because an increase in current will result in a stronger magnetic field (represented by "B"), which will cause the electrons to travel in a tighter, more compact circular path.

Therefore, based on equation 1, we can conclude that increasing the current to the coils will indeed make the circular path smaller, as you predicted. This supports your initial understanding that increasing the current will make the circle larger.

It is important to note that this equation assumes a constant magnetic field strength and voltage. If these values were to change, the relationship between current and circular path may also change.

In summary, as a scientist, it is crucial to use mathematical equations to support our hypotheses and observations. In this case, equation 1 helps us understand the relationship between current and the circular path of electrons, and supports the prediction that increasing current will make the circle smaller.