# Potential difference of an electron

• zbtzylong
In summary, the conversation discusses finding the potential difference needed for an electron to achieve a speed of 46.0% of the speed of light, starting from rest. The correct formula to use is V = (mv^2)/(2q), taking into account the relativistic mass of the electron.
zbtzylong

## Homework Statement

Through what potential difference would an electron need to be accelerated for it to achieve a speed of 46.0% of the speed of light, starting from rest? The speed of light is
c= 3.00 x 10^8 m/s
m_e = 9.11 x 10^-31 kg
|e| = 1.60 x 10^-19 C

V= Ed

## The Attempt at a Solution

1. I tried to break down E into E= F/q.
2. F=ma
3. V = (ma/q)d
5. V = m(d/t^2)d/q
6. V = m(d^2/t^2)/q
7. V = m(d/t)^2/q
8. V = mv^2/q

I plugged in the numbers using this and didn't get the right answer. Am I just going at this all wrong?

Last edited:
You are going about this problem in a convoluted way, and may be making some mistakes along the way. Try this:

Remember that the kinetic energy gained by an electron going through a potential difference, V, is equal to the potential energy lost:

$$K_{gained}= U_{lost}=qV$$

Now, how much energy would an electron need to gain to go the given speed?

Using your K=qV formula, I worked the other way around.

K=1/2mv^2

Thus,

1/2mv^2 = qV
V = (mv^2)/(2q)

Using this, I still didn't get the correct answer.

Try using M = m/$$\sqrt{1 - (v/c)^2}$$

zbtzylong said:

michalll said:
Try using M = m/$$\sqrt{1 - (v/c)^2}$$

This is probably your source of error. You need to use the relativistic mass of the electron, since you are moving at a significant fraction of the speed of light.

Nice catch michalll.

## 1. What is potential difference of an electron?

The potential difference of an electron is the difference in electric potential between two points in an electric circuit, which is measured in volts. It represents the energy gained or lost by an electron as it moves through a circuit.

## 2. How is potential difference related to voltage?

Potential difference is another term for voltage, and they are used interchangeably. Voltage is the potential difference between two points in an electric field and is the force that drives the flow of electrons through a circuit.

## 3. What factors affect the potential difference of an electron?

The potential difference of an electron is affected by the electric field strength, the distance between two points, and the charge of the particles involved. Additionally, the material and temperature of the conductor can also impact the potential difference.

## 4. How is potential difference measured?

Potential difference is measured using a voltmeter, which is connected in parallel to the component or circuit being measured. The voltmeter measures the difference in electric potential between two points and displays it in units of volts.

## 5. What is the role of potential difference in an electric circuit?

Potential difference is essential in an electric circuit as it provides the driving force for the flow of electrons. It is the difference in potential energy that allows electrons to move from the negative terminal of a power source to the positive terminal, powering the circuit.

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