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Electric Potential : Point Charge & Multiple Charge System

An electric field is also described as the electric force per unit charge. In this session, let us know electric potential due to a point charge, electric potential due to multiple charges, and also to derive an expression for the electric field at a point due to a system of n point charges.

What is Electric Potential?

Electric potential is defined as the amount of work needed to move a unit charge from a reference point to a specific point against the electric field. When an object is moved against the electric field, it gains some amount of energy which is defined as the electric potential energy. The electric potential of the charge is obtained by dividing the potential energy by the quantity of charge.

Strength of the electric field depends on the electric potential. It is independent of the fact of whether a charge should be placed in the electric field or not. Electric potential is a scalar quantity. At point charge +q, there is always the same potential at all points with a distance r. Let us learn to derive an expression for the electric field at a point due to a system of n point charges.

The electric potential of an object depends on these factors:

• Electric charge the object carries.
• The relative position with other electrically charged objects.

Electric Potential Due to a Point Charge

The electric potential at a point in an electric field is the amount of work done moving a unit positive charge from infinity to that point along any path when the electrostatic forces are applied. Suppose that a positive charge is placed at a point. The charge placed at that point will exert a force due to the presence of an electric field.  The electric potential at any point at a distance r from the positive charge +q is shown as:

$$\begin{array}{l} V = \frac{1}{4\pi ϵ_0}\frac{q}{r}\end{array}$$

Where r is the position vector of the positive charge and q is the source charge.

As the unit of electric potential is volt, 1 Volt (V) = 1 joule coulomb-1(JC-1)

When work is done in moving a charge of 1 coulomb from infinity to a particular point due to an electric field against the electrostatic force, then it is said to be 1 volt of the electrostatic potential at a point.

Electric Potential Due to Multiple Charges

Electric potential due to a system of 3 point charges

Learn to derive an expression for the electric field at a point due to a system of n point charges. When there is a group of point charges say q1, q2, q3,….qn is kept at a distance r1, r2, r3,……rn, we can get the electrostatic potential at any particular point. We can find the electrostatic potential at any point due to each individual charge by considering the other charges absent. We then add all the charges algebraically.

Hence, the electric potential at a point due to a group of point charges is the algebraic sum of all the potentials due to individual charges.

It is given as,

$$\begin{array}{l}V = \frac{1}{4\pi ϵ_0} \sum\limits_{i=1}^{n} \frac{q_i}{r_i}\end{array}$$

s

What happens to the electric potential when a negative charge is moved from point A to point B?

Electric potential increases.

What is the SI unit of electric potential?

Joules per Coulomb (Volts)

Voltmeter

E = W/Q

Electric potential energy is a scalar or vector quantity?

Scalar quantity

Hope you have learnt about electric potential due to a point charge and to derive an expression for the electric field at a point due to a system of n point charges. Stay tuned with BYJU’S for more exciting articles.

Test Your Knowledge On Electric Potential Point Charge!