Electric Potential Point Charge

To comprehend what electric potential is, one must first know what electric potential energy is. Electric potential energy is the negative of the work done by an electric force to move an object from one point to another. In layman’s terms, it’s the amount of energy required to move an object against an electric field. Electric potential is a scalar quantity which aids in the comprehension of charge movement in terms of energy. The two elements which give an object its electric potential energy are the charge it contains and its relative position in relation to other electrically charged substances.

Electric Potential

Electric potential is calculated by dividing the electric potential energy by the charge quantity. Electric potential, also referred as electrostatic potential, is the amount of work energy required to transport a unit electric charge from a reference point to a given place. 

The electric potential is determined by two factors:

The electric charge generated by the object

The object’s location in relation to other electrically charged items.

The intensity of the electric field, in essence, is determined by the electric potential. It makes no difference whether or not a charge is introduced in the electric field.

The work done per unit charge to move a unit positive test charge from infinity to that point slowly is described as electric potential at that point. At this point, we’ll suppose that the potential at infinity is zero.

V=0

Electric potential at a point is defined as work done per unit charge in order to bring a unit positive test charge from infinity to that point slowly. 

Calculation of Electric Potential

Electric Potential Due to a Point Charge

Whenever electrostatic forces are applied, the electric potential at a place in an electric field is described as the quantity of work done in transferring a unit positive charge from infinity to that point via any path. We’ll consider the charge is positive (q>0) in this case.

We have a point charge in space, and we need to determine the potential at a point ‘r’ away from the charge.

We know that a point’s electric potential is given by,

Vp=Vp–V=-pE.dr

Conventionally,

V=0

Vp=-pE.dr

We obtain, if we put the value of the electric field due to a point charge,

Vp=-pq4π0r2.dr

Vp=q4π0r2

Because of the way the charges are distributed.

Since potential is a scalar variable, the potential owing to a distribution of charges is equal to the electric potential due to point charge formula e scalar sum of the individual charges’ potential.

Vp=V1+V2+V3

Formula of electric potential due to a point charge

Electrons and other point charges are among the fundamental structures of matter. Moreover, just like a point charge, spherical charge distributions (as on a metal sphere) generate external electric fields. As a result, we must examine the electric potential generated by a point charge. Using mathematics to calculate the work required to transfer a test charge q from a huge distance to a distance of r from a point charge Q, and noting the relationship between work and potential (W=qv), it can be demonstrated that a point charge’s electric potential V is

V=kQr

Here,

 k is  a constant.

Electric Potential due to a System of Charges

Whenever dealing with a system containing several charges, we can calculate the electric potential at any given position by combining all of the potentials owing to each individual charge algebraically. Consider a set of charges denoted by the letters q1, q2, q3, and so on, with location vectors r1, r2, r3, and so on.

Electrostatic Potential Energy

The work done by an external agent in gradually changing the configuration of the system is referred to as electrostatic potential energy.

Earthing

We assume the Earth’s potential to be zero, and when a conductor is connected to the Earth, its potential is also zero. Since the Earth is always regarded as neutral, even when a great amount of charge flows to it, the net charge will remain unchanged, i.e. zero.

Things to Remember:

The energy acquired by moving an object against an electric field is referred to as electric potential.

Electric potential, also known as electrostatic potential, is the quantity of work energy required to transport a unit electric charge from a reference point to a given place.

It’s a number with a scalar value.

There are two elements that influence electric potential.

The electric charge carried by the object

The object’s location in relation to other electrically charged items.

Conclusion

Electric potential is calculated by dividing the electric potential energy by the charge quantity. Electric potential, also referred as electrostatic potential, is the amount of work energy required to transport a unit electric charge from a reference point to a given place

The work done per unit charge to move a unit positive test charge from infinity to that point slowly is described as electric potential at that point. At this point, we’ll suppose that the potential at infinity is zero.

V=0

 Electric potential is a scalar quantity which aids in the comprehension of charge movement in terms of energy. The two elements which give an object its electric potential energy are the charge it contains and its relative position in relation to other electrically charged substances.