A Brief Note on Electric Field Due To A Point Charge

The effect of an electric field on basic particles is regulated by electric charge, which is an essential element of matter. Electric charge is made up of natural units that can neither be made nor destroyed. The two forms of electric charges are positive and negative charges. When two things with an overload of one type of charge are close enough together, they repel. When two negatively and positively charged things come into proximity, they attract each other. The work done in transferring a positive unit charge from infinity to just that point against an electrostatic force of the field is defined as the electrostatic potential at any location in an electrostatic field. 

The Concept of Electric Fields

• Faraday popularised the idea of the electric field in the mid-nineteenth century. It is a vector quantity equivalent to the force a positive unit charge feels at any point P in space.
• Coulomb’s law describes the forces between charges as a direct and instantaneous interaction known as “action at a distance”. If the charges are separated at a distance then, they affect one another. We can look at it slightly differently by introducing an electric field as an intermediary between the charges. That is, the first charge sets up an electric field and the second charge placed in this electric field then the second charge experiences a force that is given by Coulomb’s law. If both charges have some nature then they will repel each other and if both have opposite nature then they will attract each other.
• Let us consider an electric charge q located in space. If we bring another charge q₀ near the charge q, then the charge q₀ experiences a force (attraction or repulsion) due to the charge q. The force experienced by q₀ is said to be due to the “electric field” set up by the charge q. Thus, the charge q creates a physical condition called ‘field’ in the space surrounding it. When placed in this field, any other charge experiences an electrical force.
• The charge q is called the “source charge”, and the charge q₀ is called the “test charge”. The source charge may be a point charge, a group of the point -charges or a continuous distribution of charges.

Electric Field Due to a Point Charge Formula

The strength of the electric field at any point is the electric field intensity at that point. It is stated as the force felt by a single positive charge at a specific location. Here, if force acting on this unit positive charge +q₀ at a point r, then electric field intensity is given by:

E(r) = F(r)/q₀

As a result, E is a vector quantity that is in the direction of the force and parallel to the movement of the test charge +q. Its standard unit is N/C.

The electric field for +q₀ is radially directed outwards from the charge, whereas the electric field for -q₀ is radially directed inwards. 

Electric Field Due to a Point Charge Examples:

EXAMPLE 1:

Suppose, on an axis; you have two charges. At what point along the axis is the electric field zero when one charge of −2μC is located at the origin while the other charge of −8μC is located at 4m?

k_e = 8.99 x 10⁹N⋅m²C²

Explanation:

The formula for an electric field from a point charge:

E = kq/r²

We set the equations for both charges equal to each other to find the point where the electric field is 0 since that is where they will cancel out each other. Let x be the location of the point. The first charge’s radius would be x, and the radius for the second one would be 4−x.