Otis Singleton
Electric potential is defined as the amount of work done in moving a test charge from infinity to a point. It is also defined as the electric potential energy per unit charge. The SI unit of electric potential is the volt (V). Electric potential difference between two points, A and B, is defined as the work done to move a positive unit charge from A to B. The SI unit of potential difference is also the volt. The electric potential calculator allows you to calculate the electric potential at a point due to a single point charge or a system of point charges.
| Characteristics | Values |
|---|---|
| What it calculates | Electric potential at a point due to a single point charge or a system of point charges |
| What it displays | Value of the electric potential at the observation point |
| Unit of electric potential | Volt (V) |
| Electric potential defined as | Amount of work done in moving a test charge from infinity to that point |
| Electric potential defined as | Electric potential energy per unit charge |
| Electric potential difference between two points | Work done to move a positive unit charge from point A to B |
| Unit of potential difference | Volt (V) |
| Electric potential difference formula | \(V_B−V_A\) |
| Electric potential formula | \(V_p = V_1 + V_2 + . . . + V_N = \sum_1^N V_i\) |
| Total energy of a system | Sum of kinetic energy and potential energy of a system |
| Electric potential difference in a circuit | Exerts a force on the charges in the wire causing a movement of charge (called current) |
| Electric potential difference calculation | Divide the total work done by the total charge |
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What You'll Learn
Electric potential difference and energy are distinct
Electric potential difference, also known as voltage, is the work done per unit charge to move a unit charge from one point to another in an electric field. It is measured using a voltmeter and its SI unit is the volt (V).
On the other hand, electric potential energy is the energy possessed by electric charges. The electric potential at a point is defined as the amount of work done in moving a test charge from infinity to that point. The SI unit of electric potential energy is the joule (J) and that of charge is the coulomb (C). Hence, the SI unit of electric potential is J/C, i.e., the volt (V).
Although both concepts are related, voltage and energy are distinct. For example, a motorcycle battery and a car battery can both have the same voltage, yet one stores much more energy than the other. This is because the energy delivered by a battery depends on the charge it can move, which is not necessarily related to its voltage.
Calculating the work done directly can be challenging due to the complex nature of the direction and magnitude of the force involved. Therefore, it is more convenient to define a quantity that allows us to calculate the work done on a charge independently of the magnitude of the charge. This quantity is known as electric potential, which is the potential energy per unit charge. By defining electric potential in this way, we can eliminate the dependence on the charge, making it independent of the test charge.
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Electric potential difference in circuits
Electric potential difference, also known as voltage, is a fundamental concept in the analysis of electrical circuits. It refers to the energy used or the work done per unit charge to move a positive charge between two points in a circuit. The SI unit of potential difference is the volt (V), and 1 volt is defined as 1 joule of work done to carry a positive charge of 1 coulomb from infinity to the point of interest against an electrostatic force.
In a circuit, electric potential difference is measured between two points, often across a specific component. Voltmeters are used to measure the potential difference, and they must always be connected in parallel with the two points being measured. The potential difference between two points in a circuit is crucial for understanding the behaviour of charges and the flow of current.
The concept of electric potential difference is distinct from electrical potential energy. Voltage represents the energy per unit charge, while potential energy refers to the total energy of a system. The relationship between potential difference and electrical potential energy is given by the equation ΔU = qΔV, where ΔU is the change in potential energy, q is the charge, and ΔV is the potential difference.
Calculating electric potential difference in circuits involves considering the work done to move a positive unit charge between two points. The formula for calculating the potential difference between points A and B is ΔV = VB – VA, where ΔV is the potential difference, and VB and VA are the electric potentials at points B and A, respectively. This calculation helps determine the energy required to move a charge between these points.
It's important to note that electric potential difference is a scalar quantity, meaning it has magnitude but no direction. Additionally, when discussing electric potential in circuits, we typically refer to potential difference rather than absolute values, as we can only measure potential differences relative to a reference point.
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Electric potential difference and energy in batteries
Electric potential difference, also known as voltage, is the energy per unit charge. It is the difference in potential energy of a charge moved from one point to another, divided by the charge. The SI unit of electric potential is the volt (V), and 1 volt means that 1 joule of work is done to carry a positive charge of 1 coulomb from infinity to that point against the electrostatic force.
In the context of batteries, the electric potential difference is called the electromotive force (EMF). The EMF of a battery is the potential difference between its two terminals. The positive terminal is at a higher voltage than the negative one. When a battery is connected to a closed circuit, current flows and encounters electrical resistance, causing a voltage drop (a loss in potential energy). This loss of potential energy is equal to the heat generated by the resistor.
The relationship between potential difference (voltage) and electrical potential energy is given by the equation:
\[ \Delta V = \frac{\Delta PE}{q} \]
\[ \Delta PE = q \Delta V\]
Where:
- \(\Delta V\) is the potential difference (in volts)
- \(\Delta PE\) is the change in potential energy (in joules)
- \(q\) is the charge (in coulombs)
For example, consider a 12.0 V car battery running a 30.0 W headlight. The battery loses energy, so the change in potential energy (\(\Delta PE\)) is -30.0 J. Since the electrons are moving from the negative terminal to the positive, the potential difference (\(\Delta V\)) is +12.0 V.
It is important to distinguish between potential difference and electrical potential energy. While they are related, they are not the same thing. A motorcycle battery and a car battery may have the same voltage but differ in the amount of energy they can deliver. This is because the total energy delivered depends on the amount of charge the battery can move.
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Electric potential difference and electrostatic force
Electric potential and electric potential energy are not the same things. Electric potential energy is the energy per unit charge, whereas electric potential is the electric potential energy per unit charge. The SI unit of electric potential is the volt (V).
The electric potential difference between two points, A and B, is defined as the work done to move a positive unit charge from A to B. The SI unit of potential difference is also the volt.
The electric potential at a point P due to a charge q is inversely proportional to the distance between them. Hence, when the distance is infinite, the electric potential is zero.
The electrostatic force is a conservative force, meaning that the work done on q is independent of the path taken. This is analogous to the gravitational force in the absence of dissipative forces such as friction. When a force is conservative, it is possible to define a potential energy associated with the force. It is usually easier to deal with the potential energy (because it depends only on position) than to calculate the work directly.
The work done against the electrostatic force of interaction equals an increase in the system's potential energy. The work done to displace the charge is stored as potential energy, which is known as electric potential energy or electrostatic potential energy.
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Calculating electric potential difference with a calculator
Electric potential and electric potential energy are not the same things. Electric potential energy is calculated using the standard potential energy formula, E=mgh. However, electric potential is defined as the electric potential energy per unit charge.
The SI unit of electric potential is the volt (V). We can say that the electric potential at a point is 1 V if 1 J of work is done in carrying a positive charge of 1 C from infinity to that point against the electrostatic force. The unit of potential difference is also the volt.
The electric potential difference between two points A and B is defined as the work done to move a positive unit charge from A to B. The SI unit of potential difference is volt (V). Electric potential is a scalar quantity as it has no direction.
The electric potential calculator allows you to work out the electric potential at a point due to a single point charge or a system of point charges. You can also use this tool to find out the electrical potential difference between two points.
To calculate the electric potential at any point A due to a single point charge, we use the formula:
VA = k * q / r
Where:
- VA is the electric potential at point A
- K is the electrostatic constant
- Q is the charge
- R is the distance between the charge and the point
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Frequently asked questions
An electric potential difference calculator is a tool that allows you to calculate the electric potential at a point due to a single point charge or a system of point charges.
The formula for calculating electric potential difference is to divide the total work done by the total charge.
The SI unit of electric potential difference is the volt (V).
Electric potential difference is also known as voltage. Voltage is the energy per unit charge.
