# Why do we need to take the absolute value of charge in an electron gun?

• ChiralSuperfields
In summary, the conversation discusses the solution to a problem involving electric potential and energy conservation. The solution uses a negative potential to accelerate electrons and increases their kinetic energy. The reason for this is that the electric potential energy of the electrons decreases as they move to a higher potential.
ChiralSuperfields
Homework Statement
Relevant Equations
For part (a) of this problem,

The solution is,

However, why did they need to take the absolute value of the charge? I thought they could keep the original signs as shown below:

Using energy conservation, the electric force dose internal work transferring electric potential energy into kinetic energy

Thanks for any help!

The velocity before the electron transited the potential gradient was zero. Your energy equation should read ##\Delta KE+\Delta EPE=0##.
To accelerate the electrons, the gun must have a negative potential, so ##\Delta V=+2500V##.
This gives ##\Delta KE=-q\Delta V##.
The given solution used the knowledge that the field increases the KE in a different way. Instead of taking the trouble to manage the signs correctly, it just forced everything positive.

ChiralSuperfields
haruspex said:
To accelerate the electrons, the gun must have a negative potential, so ##\Delta V=+2500V##.
Thank you @haruspex! Are you saying that V_i = -2500V and V_f = 0? Why must gun have negative potential and therefore Delta V = 2500V?

Callumnc1 said:
Why must gun have negative potential
So as to repel the electrons.

ChiralSuperfields
haruspex said:
So as to repel the electrons.
Thanks for the reply @haruspex! I'm assuming that at V_i = -2500V there is no protons and a finite number of electrons. And at V_f = 0 there is no electrons and protons, correct?

However, if the gun has negative potential, then the electric potential energy of the electrons will increase over the gun as delta V is positive. However, how is this possible since the kinetic energy also increases? Where dose this energy that turns into kinetic energy come from?

Callumnc1 said:
if the gun has negative potential, then the electric potential energy of the electrons will increase over the gun as delta V is positive
Don’t confuse electric potential with electric potential energy.
When a negative charge moves to a higher potential it loses electric potential energy. ##\Delta E=q\Delta V##.

ChiralSuperfields
haruspex said:
Don’t confuse electric potential with electric potential energy.
When a negative charge moves to a higher potential it loses electric potential energy. ##\Delta E=q\Delta V##.
Oh got it now! Thanks again @haruspex!

berkeman

## 1. Why is the absolute value of charge important in an electron gun?

The absolute value of charge is important in an electron gun because it determines the direction and strength of the electric field that accelerates the electrons. By taking the absolute value, we can ensure that the electrons will always be accelerated in the same direction, regardless of their initial charge.

## 2. How does the absolute value of charge affect the beam of electrons in an electron gun?

The absolute value of charge affects the beam of electrons in an electron gun by determining the amount of force that the electric field will exert on the electrons. A higher absolute value of charge will result in a stronger electric field and a more focused and powerful beam of electrons.

## 3. Can the absolute value of charge be negative in an electron gun?

No, the absolute value of charge cannot be negative in an electron gun. The absolute value of charge is always a positive quantity, as it represents the magnitude of the charge without indicating its direction. In an electron gun, the charge of the electrons is always negative, but by taking the absolute value, we are only concerned with the magnitude of the charge.

## 4. How is the absolute value of charge determined in an electron gun?

The absolute value of charge is determined by the amount of voltage applied to the electron gun. The higher the voltage, the stronger the electric field and the higher the absolute value of charge on the electrons. This can be controlled and adjusted by the user to achieve the desired beam intensity and focus.

## 5. What would happen if the absolute value of charge is not taken into account in an electron gun?

If the absolute value of charge is not taken into account in an electron gun, the electrons may not be properly accelerated and may not form a focused beam. This can result in a weaker and less precise beam, affecting the accuracy and effectiveness of the electron gun in its intended purpose.

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