Electric Field

If we place a test body carrying a positive electric charge q near a charge rod, an electrostatic force F will act on it. We speak of an electric field in this region. We represent it by a vector E defined by

            E= F/q
Electric field at a point is defined as the force that acts on a unit positive charge place at that point.

The direction of the vector E is that of vector F. The SI unit for the electric field is the Newton/coulomb (NC^-1) or volt/meter (Vm ^-1).

Several other terms are commonly used, for example, electric field strength, electric field intensity or intensity of the electric field. The words “strength” or “intensity” are really unnecessary.

F = q E
i.e., the force F exerted on a charge q at a point where the electric field is E equals the product of the electric field and the charge.

For a configuration which has a number of discrete stationary charges, the net electric field at a point is the vector sum of the individual electric fields due to each charge. Thus

E = E₁ + E₂ + E₃ + … = ∑ E_i
= ____1____ [ q¹  r1 + q²  r2 + q³ r3 + …. ]
    4П ε₀_____ q²₁___r²₂____r²₃

=   ____1____ ∑ q_i  r_i
       4П ε₀  ______i  r²_i

For a continuous charge distribution, the electric field E at any point is given by

    E = ____1____ ∫ dq r
               4П ε0  __   r²