Electric Potential : Point Charge & Multiple Charge System

Electric potential is mainly a characteristic of the electric field. It is independent of the fact 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 \(r\).

Electric Potential due to a Point Charge:

The electric potential at a point in an electric field is defined as the amount of work done in 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:

It is given by,

\( V = \frac{1}{4\pi ϵ_0}\frac{q}{r}\)

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

Electric potential due to a system of 3 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,

\(V\) = \(\frac{1}{4\pi ϵ_0} \sum\limits_{i=1}^{n} \frac{q_i}{r_i}\)

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