**ELECTRIC FIELD (NCERT 12 ^{TH} PHYSICS PART 1)**

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

where **r**ˆ = **r**/r, is a unit vector from the origin to the point r. Thus, Eq.(1.6) 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

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**) (1.8)

Equation (1.8) defines the SI unit of electric field as N/C*.

Some important remarks may be made here:

(i) From Eq. (1.8), 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 at that point*. The charge *Q, *which is producing the electric field, is called a *source charge *and the charge *q, *which tests the effect of a source charge, is called a *test charge*. Note that the source charge *Q *must remain at its original location. However, if a charge *q *is brought at any point around *Q*, *Q *itself is bound to experience an electrical force due to *q *and will tend to move. A way out of this difficulty is to make *q *negligibly small. The force F is then negligibly small but the ratio F/*q *is finite and defines the electric field:

A practical way to get around the problem (of keeping *Q *undisturbed in the presence of *q*) is to hold *Q *to its location by unspecified forces! This may look strange but actually this is what happens in practice. When we are considering the electric force on a test charge *q *due to a charged planar sheet (Section 1.15), the charges on the sheet are held to their locations by the forces due to the unspecified charged constituents inside the sheet.

(ii) Note that the electric field E due to *Q*, though defined operationally in terms of some test charge *q, *is independent of *q*. This is because F is proportional to *q*, so the ratio F/*q *does not depend on *q*. The force F on the charge *q *due to the charge *Q *depends on the particular location of charge *q *which may take any value in the space around the charge *Q. *Thus, the electric field E due to *Q *is also dependent on the space coordinate r. For different positions of the charge *q *all over the space*, *we get different values of electric field E. The field exists at every point in three-dimensional space.

(iii) For a positive charge, the electric field will be directed radially outwards from the charge. On the other hand, if the source charge is negative, the electric field vector, at each point, points radially inwards. (iv) Since the magnitude of the force F on charge *q *due to charge *Q *depends only on the distance *r *of the charge *q *from charge *Q*, the magnitude of the electric field E will also depend only on the

distance *r*. Thus at equal distances from the charge *Q*, the magnitude of its electric field E is same. The magnitude of electric field E due to a point charge is thus same on a sphere with the point charge at its centre; in other words, it has a spherical symmetry.