# Electric Potential

Electric potential is a term used to describe the amount of work needed to move a charged particle from one point to another. It’s a scalar quantity, meaning it doesn’t have a direction. But the electric charge of the particle does have a sign that relates to its charge. So, if you’re trying to move a charged particle, you need to know its electric potential and its charge to get the job done. This is where electric potential comes in handy, as it helps you understand how much work you need to do to move a charged particle.

## Characteristics of electric potential

Electric potential is a measure of the energy required to move a charged particle. If there's an isolated positive charge, the electric potential around it is positive. On the other hand, if there's an isolated negative charge, the electric potential around it is negative. And if you look at the charge from a really far distance, the electric potential is zero. This means that the energy required to move a charged particle is zero when you're at an infinite distance from the charge. So, electric potential helps you understand how the energy to move a charged particle changes based on its location in relation to the charge.

### Electric potential in a field

The electric potential of a point charge (q) in a field depends on the charge creating the potential, the distance from the point charge, and the permittivity. This is shown by the equation: V = Q/(4πεo r), where V is the electric potential in volts, Q is the point charge, r is the distance in metres, and εo is the permittivity of a vacuum in Farad/metre.

For a positive charge q, the electric potential increases when the distance r decreases, as more work is needed to move the charge due to the repulsive force. For a negative charge q, the electric potential decreases when the distance r decreases, as the attractive force makes it easier for a positive test charge to move. This is illustrated below, where the interaction between a positive and negative charge is shown.

To find the potential at a point caused by multiple charges, you have to find the sum of the potential from each charge.

## What is electric potential energy?

Electric potential energy is the energy required to move a charge (q) from one point to another in an electric field. Moving a positive charge closer to another positive charge requires work to overcome the repulsive force, while moving a positive charge away from a negative charge requires work to overcome the attractive force. The energy transferred to the moving charge is referred to as electric potential energy.

The amount of electric potential energy is proportional to the strength of the electric field. A stronger electric field requires more energy to move the charge through the field, resulting in a larger electric potential energy. Thus, electric potential energy helps us understand the amount of work required to move a charge through an electric field and the relationship between the strength of the field and the amount of energy required.

### Electric potential energy for two point charges

The electric potential of a pair of point charges is proportional to the product the two charges, as shown in the equation: V = (kQq)/r, where V is the electric potential in volts, Q and q are the magnitudes of the two point charges in Coulombs, r is the distance between the two charges measured in metres, and k is Coulomb's constant, which is equal to 1/(4πε0) and has a value of approximately 9 x 10^9 Nm^2/C^2.

The vacuum permittivity ε0 is a constant that represents the ability of electric fields to permeate through a vacuum. It has a value of approximately 8.85 x 10^-12 F/m and is measured in Farads per metre. The product of the two charges and the distance between them determine the strength of the electric potential between the charges. The larger the product of the charges or the smaller the distance between them, the larger the electric potential.

### Electric potential and work

The electric potential can also be expressed mathematically in terms of work. The work required to move a charge through an electric field is equal to the product of the electric potential and the charge causing the electric potential. Mathematically, this can be expressed as:

W = QΔV

Where W is the work done in jou the charge in Coulombs, and Δ potential in volts. This equation shows that the work done in moving a charge through an electric field is proportional to the electric potential difference across the field and the magnitude of the charge. If the electric potential difference is large, then more work is required to move the charge through the field. Similarly, if the charge is larger, more work is required to move it through the field.

## What is the electric potential gradient?

The electric potential gradient is an important concept in understanding electric fields. It refers to the change in electric potential per unit distance in a particular direction. Mathematically, the electric potential gradient is the negative derivative of the electric potential with respect to distance. In other words, it is the rate of change of the electric potential as you move along a particular direction.

Equipotential lines, which are represented by the orange circular dotted lines in the illustration, are surfaces in an electric field that have the same electric potential. They are always perpendicular to electric field lines, which are illustrated with blue lines. Equipotential lines express the strength of the electric potential at different points in the field. The denser the equipotential lines, the stronger the potential.

Together, the electric potential gradient and equipotential lines provide a way to visualize and understand the behavior of electric fields. By analyzing the shape and density of equipotential lines, we can determine the strength and direction of the electric field at any point in space.

## What is electric potential difference?

Electric potential difference is a measure of the work required to move a charged particle in an electric field from one point to another. It is given by the equation:

ΔV = - E ∆r

where ΔV is the potential difference, E is the electric field strength, and ∆r is the distance between the two points of interest. The negative sign indicates the direction of the electric field, which is always outwards from a positive charge and inwards towards a negative charge.

To solve the given problem, we need to find the electric potential at a distance of 25 cm from the generator, which has a radius of 10 cm and generates a potential of 150 kV.

First, we can find the total charge of the generator using the potential equation:

ΔV = - E ∆r
150,000 = - E (0.25)
E = -600,000 V/m

The electric field strength is therefore -600,000 V/m.

Next, we can find the potential at a distance of 25 cm from the generator, which is the sum of the potential due to the generator to the +_point
V_gen = kQ/r_gen
V_point = kQ/r_point

where k is Coulomb's constant, Q is the charge of the generator, r_gen is the radius of the generator, and r_point is the distance from the generator to the point of interest.

We can find the charge of the generator using the potential equation:

V_gen = kQ/r_gen
150,000 = (9 x 10^9) Q / 0.1
Q = 1.67 x 10^-5 C

Substituting this value into the equation for the potential due to the point of interest, we get:

V_point = kQ/r_point
V_point = (9 x 10^9) (1.67 x 10^-5) / 0.25
V_point = 6.01 x 10^5 V

Therefore, the electric potential at a distance of 25 cm from the generator is:

V = V_gen + V_point
V = 150,000 + 601,000
V = 751,000 V

In summary, the electric potential at a distance of 25 cm from the generator is 751,000 V.

## Electric Potential - Key takeaways

You are correct! Electric potential is defined as the amount of work required to move a unit of positive charge from one point in an electric field to another, against the electric field. Its unit is volts (V).

The electric potential difference, also known as voltage, is the difference in electric potential between two points in an electric field. It is measured in volts (V) and is given by the equation:

ΔV = V2 - V1

where ΔV is the potential difference, V2 is the potential at the second point, and V1 is the potential at the first point.

As you mentioned, the electric potential decreases as the distance between the point under study and the electric potential source increases. This is because the electric field strength decreases with distance from the source, causing a decrease in the amount of work required to move a unit of positive charge.

## Electric Potential

What is electric potential?

Electric potential is the work required to move a charge.

How do you find electric field strength from potential?

You can find electric field strength once you know the electric potential and the separation between two points, A and B. Then you use the formula E=VAB/d.

What is the difference between electric potential and potential difference?

The electric potential is the work required to move a point charge in from an electric field. Potential difference is the change in electric field strength.

What is the unit for electric potential?

Electric potential is measured in Volts.

Is electric potential a scalar or vector quantity?

Electric potential is a scalar quantity.