Electric field due to a point charge

Introduction

The electric field due to a point charge is a region of space around a charged particle or between two voltages that exerts a force on charged items nearby.

The electric potential is a metric for how much energy is stored per unit of charge.

Electric potential energy is the amount of energy gained when an object moves against an electric field. For each charge, the electric potential is determined by dividing the potential energy by the charge quantity.

For a uniform field, the relationship between the electric field (E), the potential difference between points A and B (ϕ), and the distance between points A and B (d) is: 

E = − d

The magnitude of the electric field E created by a point charge Q is E = K|Q|r2

Where r is the distance from Q, and K is the coulomb constant.  ( K = 140)

 Fields owing to many charges add like vectors, and the electric field E is a vector.

Electric Field

The electric field E is a vector quantity that can be found at any point in the universe. If a test charge were placed, then the force applied on that charge is represented by the electric field at that location. 

Electric Field due to a point charge

Faraday was the first to introduce the concept of the field.

The strength of the electric field due to a point charge is the electric field intensity at that point.

It is defined as the force that a unit positive charge feels when it is placed at a specific spot.

Consider a point charge Q that is kept in a vacuum at the origin O. According to Coulomb’s law, if another point charge q is kept at a position P from the charge Q, where OP = r, the charge Q will create an electrostatic force on q. The charge Q creates an electric field that acts all around the place. The field at point P generates a force and acts on a fresh charge, q. The electric field produced by a charge Q at r can be calculated in the following way:

  E(r) = 140Qr2 r

Where r is a unit vector from the origin to r, as a result, for each value of the position vector r, the above statement provides the electric field value.

The presence of an electric field due to a point charge is related to the action of a charge.

The force F that a charge Q exerts on another charge q is computed as:

 F(r) = 140Qqr2 r

If the charge q is symbolised by the vector r, it feels a force F equal to the charge q multiplied by the electric field E at the location of q.

As a result, F(r) = q x E(r)

Electric field due to a system of charges

The vector sum of the electric fields at a point due to all the individual charges is the electric field at a point due to a system of charges.

Consider a system of charges q1, q2,…, qn with r1, r2,…, rn  location vectors with respect to some origin O. The electric field at a point in space due to a system of charges, analogous to the electric field at a point in space due to a single charge, is described as the force experienced by a unit test charge placed at that point without changing the original placements of charges q1, q2,…, qn. We have to use Coulomb’s law and the principle of superposition. 

The electric field E1 caused by q1 at r1 is expressed as,

E1(r) = 140q1r12 r1

Here r1 is the distance between q1 and P, and  r1  is the unit vector in the direction from q1 to P.

In the same way, the electric field E2 cause by  q2 at r2 can be written as,

E2(r) = 140q2r22 r2

Here r2 is the distance between q2 and P and r2  is the unit vector in the direction from q2 to P. Charges q3, q4…, qn cause similar expressions for fields E3, E4…, En . The electric field E due to the system of charges can be represented as follows using the superposition principle:

E(r) =  E1 + E2 + E3 …………+ En .     ( All in vector form )

The source charge positions determine E, which is a vector variable that varies from one location in space to another.

Electric Potential

The difference in potential energy per unit charge between two points in an electric field is known as the electric potential difference between the two points.

EnergyCharge Equals electric potential difference (V)

Volt is the SI unit of electric potential.

Electric potential due to a point charge

When electrostatic forces are applied, the amount of work done in transferring a unit positive charge from infinity to that point along any path is known as the electric potential of that point charge.

V = KQr gives the electric potential V of a point charge.

Here K is the coulomb constant, Q is the charge , r is the distance of the point from the charge

Electric potential due to multiple charges

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

It’s written as,

V =  KQ1r1 + KQ2r2 + KQ3r3 ……. + KQnrn

Electric Potential Energy

The capacity for accomplishing work that emerges from location or configuration can be characterised as electric potential energy. A charge exerts a force on any other charge that is in the electrical situation, and electric potential energy comes from any collection of charges. If a positive charge Q is fixed at a certain position in space, every other positive charge brought close to it will suffer a repulsive force and have potential energy.

In the region of this source charge, the potential energy of a test charge q will be:

U = KQqr

Conclusion

The force that a unit positive charge would experience if put at that location in space can be defined as the electric field due to a point charge Q at that point in space. A source charge Q generates an electric field, while a test charge q assesses the effect of a source charge Q. The electric field due to a point charge Q at a location r is given by

 E(r) = 140Qqr2 r

The amount of work energy necessary to shift a unit of electric charge from a reference point to a specific place in an electric field is known as electric potential energy.