Current Electricity-Applications-Electric Potential

The electric potential is a characteristic of the electric field by some electric charge configuration. The concept of potential energy in mechanics significantly helps to connect the conservative forces of nature like the gravitational force, elastic force by the spring, etc. Similarly, in electrostatics, scientists define another scalar quantity known as the electric potential denoted by V. This is highly useful to describe electrostatic phenomena. 

Definition

So, what is electric potential?

Let us look at the definition of electric potential. Many corollary forms of electric potential exist. Some of them are as follows:

Electric potential between points A and B is defined as the amount of work done carrying a unit test positive charge from point A to B without any acceleration. The definition says without any acceleration because otherwise, some extra energy will be needed to provide the acceleration.

Mathematically, V=w/q

The electrostatic potential difference between points A and B is 1 volt if 1 joule of work is needed to move a positive unit charge from one point to another against the electrostatic force without any acceleration.  

Alternative definition

Electrostatic potential at any point says A in a region of the electric field is defined as the minimum amount of work needed to carry a unit positive charge from infinity to that point.

The electrostatic potential is a scalar quantity because it has no direction. The SI unit of electrostatic potential is Volt (V).

1V=1Joule/1 C 

Relation between electric intensity and electric potential:

dV = ─ E dx or,

⇒E=−dV/dx

The negative sign signifies that the electric field is in the direction of decreasing potential.

Electric potential due to a point charge:

Assume a point charge q placed at any arbitrary point A.

Consider a point p situated at some distance x from A.

The magnitude of the electrostatic force on the unit-positive charge at A is

Let us assume a point charge q placed at a point A.

Let P be an arbitrary point at a distance x from A.

As per the definition, the electric field at P from point A is defined as E=1/ 4πε0x2

Work done to move the particle by a small distance dx is given by:

dW=E.dx

On putting the values and integrating from infinity to x we get

W=1/ 4πε0x

Note: If A is situated at infinity i.e at a very large distance from P then the value of electric potential tends to 0.

Potential at a point due to a single charge is spherically symmetric.

The electric potential varies inversely with the distance. It tends to be 0 at infinity. Also, the electric potential can be both positive and negative, including 0.

Electric potential due to multiple charges: Let q1,q2,q3……..qnbe n electric charges present at distances r1,r2,r3…..rn from point p.Then the electric potential at point p due to the point charges is given by V=K(q1/r1+q2/r2+q3/r3+………qn/rn)

Characteristics of Electric Potential

1. The electric potential is a scalar quantity so it does not have any direction.

2. Electric potential either decreases or remains constant with distance from the source charge.
3. It is conservative. Hence the work done in moving any charge from one point to another and then moving back to the same initial point is 0

In other words, the work done in an electric field is 0.

4. It is defined after taking any point as a reference. Generally, the electric potential at infinity is taken as 0 for reference.
5. The surfaces on which the electric potential is the same are known as equipotential surfaces. The work done in moving any charge in the equipotential surface is 0.

Example

1. Suppose a point charge 1 C is placed at origin O. Calculate the electric potential at a distance of 2m from the point charge.

=We assume the electric potential at infinity to be 0.

So the required electric potential is=kq/r

=9.1*109 *½ V

=4.55*109 V

2. Suppose a point charge q is taken from point A to B followed by C then back to A in an equipotential surface. What is the work done by the external agent?

= The electric field is conservative. Hence work done in moving a charge does not depend on the path adopted. Also, the work done in moving a charge in the equipotential surface is 0. Hence, the net work done by the external agent is 0;

Conclusion

The electrostatic potential is a defined physical quantity to understand the phenomenon related to electrostatics. The electric potential has many definitions. Electric potential Between two points A and B is defined as the amount of work done in carrying unit test positive charge from point A to B without any acceleration. The definition says without any acceleration because otherwise some extra energy will be needed to give the acceleration. Its SI unit is Volt and is denoted by V. It is a scalar quantity because it is independent of the directions. The electric field is conservative. So, the work done in moving any charge through the field is independent of the path adopted.