. E LECTRIC F IELD Let us consider a point charge Q placed in vacuum, at the origin O. If we place another point charge q at a point P, where OP = r , then the charge Q will exert a force on q as per Coulomb’s law. We may ask the question: If charge q is removed, then what is left in the surrounding?
Is there nothing? If there is nothing at the point P, then how does a force act when we place the charge q at P. In order to answer such questions, the early scientists introduced the concept of field . According to this, we say that the charge Q produces an electric field everywhere in the surrounding.
When another charge q is brought at some point P, the field there acts on it and produces a force. The electric field produced by the charge Q at a point r is given as ( ) ˆ ˆ Q Q E r ( . ) where ˆ = r /r, is a unit vector from the origin to the point r . Thus, Eq.( .
) specifies the value of the electric field for each value of the position vector r . The word “field” signifies how some distributed quantity (which could be a scalar or a vector) varies with position. The effect of the charge has been incorporated in the existence of the electric field. We obtain the force F exerted by a charge Q on a charge q , as ˆ Qq F ( .
) Note that the charge q also exerts an equal and opposite force on the charge Q. The electrostatic force between the charges Q and q can be looked upon as an interaction between charge q and the electric field of Q and vice versa. If we denote the position of charge q by the vector r , it experiences a force F equal to the charge q multiplied by the electric field E at the location of q. Thus, F ( r ) = q E ( r ) ( .
) Equation ( . ) defines the SI unit of electric field as N/C * . Some important remarks may be made here: (i) From Eq. ( .
), we can infer that if q is unity, the electric field due to a charge Q is numerically equal to the force exerted by it. Thus, the electric field due to a charge Q at a point in space may be defined as the force that a unit positive charge would experience if placed * An alternate unit V/m will be introduced in the next chapter. FIGURE . Electric field (a) due to a charge Q , (b) due to a charge –Q .