# Potential Difference in case of electrons

• Miraj Kayastha
In summary, when an electron passes from A to B, it gains energy because in W = Q . V, Q is negative.
Miraj Kayastha
If the potential difference between point A and point B is 10 Volts, then when a unit positive charge passes from A to B, the charge loses 10 J of energy.

But when an electron passes from A to B does it gain energy, because in W = Q . V , Q is negative.

I am really confused in potential difference and in the formula W = Q . V.

I have seen in some books that when electron is said in the question the calculation use the value of positive elementary charge, why is it so?

In physics the current is defined in terms of a positive flow of charge; in ordinary wires and batteries this positive current is the negative of the actual flow of electron charge.

In some engineering contexts they concentrate on the electron flow; in this case they use a different convention: the positive current is the flow of electrons. Hence they are treating the electrons as "positive" in some sense. This is useful when you are studying electronic devices.

The question of "work done by" or "work done on" requires a change of sign. But the absolute values are the same.

So you just have to understand the conventions being used by the text.

You must be confused (or may be the book is confused). The electron has negative charge so, as you suspected, an increase of its potential V corresponds to a decrease of its potential energy U because U = q V and q is negative for an electron.

When an electron is accelerated across a gap with a PD across it, it ends up with KE. When it passes through a resistance, the small amount of KE that it gains, is negligible. In both cases, eV energy is supplied (and transferred) so the work done (force times displacement, in the end) on it is positive.
You can be confident that there is no self contradiction in the system. All you need to do is to go over your problem and take strict account of the signs. This will give you the right answer, which will be that work is done on the electron in both cases. The resulting energy of the electron is either passed on to the material of the resistor (heating) or on the material of the Anode (heat, also).
If your book seems to be getting it wrong, look at another book and that may resolve your difficulty.

I can explain the concept of potential difference and how it applies to electrons. Potential difference is a measure of the difference in electric potential energy between two points in an electric field. It is often denoted as V and is measured in volts (V).

In the case of electrons, the potential difference between two points is still measured in volts. However, the direction of the electric field is opposite to that of the direction of the electron's motion. This results in a negative value for the potential difference. So, when an electron moves from point A to point B, it will experience a decrease in electric potential energy and gain kinetic energy. This is because the electric field is doing work on the electron, giving it energy.

In the formula W = Q . V, Q represents the charge and V represents the potential difference. As you mentioned, for electrons, Q is negative. This is because the charge of an electron is opposite to that of a positively charged particle. So, when we plug in the values for Q and V, we get a negative value for the work done on the electron. This means that the electron is gaining energy as it moves from point A to point B.

In some textbooks, the value of positive elementary charge is used instead of the negative value for Q. This is because it simplifies the calculation and gives the same result. However, it is important to remember that in the case of electrons, Q will always be negative and the work done on the electron will always be positive.

I hope this explanation helps to clarify the concept of potential difference in the case of electrons. It is a fundamental concept in the study of electricity and is crucial in understanding the behavior of electric charges in an electric field.

## 1. What is potential difference in the case of electrons?

Potential difference, also known as voltage, is the difference in electric potential energy between two points in an electric circuit. In the case of electrons, it refers to the difference in energy levels between the negative and positive terminals of a battery or power source.

## 2. How is potential difference measured?

Potential difference is measured in units of volts (V) using a voltmeter. The voltmeter is connected in parallel to the component or circuit being measured and the reading on the voltmeter indicates the potential difference.

## 3. What is the relationship between potential difference and current?

Potential difference and current are directly proportional, according to Ohm's law. This means that as potential difference increases, the current also increases. In other words, a higher potential difference will result in a greater flow of electrons through a circuit.

## 4. Can potential difference be negative?

Yes, potential difference can be negative. This occurs when the direction of electron flow is opposite to the direction of conventional current flow. In this case, the potential difference is negative because the electrons are losing energy as they flow through the circuit.

## 5. How does potential difference affect the movement of electrons?

Potential difference is the driving force for the movement of electrons in a circuit. The greater the potential difference, the more energy the electrons have and the faster they can move through the circuit. This is why higher potential differences are needed for larger currents or for electricity to travel over longer distances.

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