Consider a point charge Q1 as shown in figure:

If any other similar charge Q2 is brought near it Q2 experiences a force. Infact if Q2 is moved around Q1 still Q2 experiences a force as shown in figure.

Thus, there exists a region around a charge in which it exerts force on any other charge. This region where a particular charge exerts a force on any other charge located in that region called electric field of that charge. The electric field of Q1 is shown in figure (b).

The force experienced by the charge Q2 due to Q1 is given by Coulombs law as ,

 = Q1 Q2 / 4 π R² 12  .

Thus, force per unit charge can be written as:

 /Q2 = Q1 / 4 π R² 12  .

This force exerted per unit charge is called electric field intensity or electric field strength. It is a vector quantity and is directed along a segment from the charge Q1 to the position of any other charge.

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It is denoted as .

Another definition of electric field is the force experienced by a unit positive test charge that is Q2 = 1C.

Consider a charge Q1 as shown in figure below. The unit positive charge Q2=1C is placed at distance R from Q1. Then the force acting on Q2 due to Q1 is along the unit vector  As the charge Q2 is unit charge the force exerted on Q2 is nothing but electric field intensity  of Q1. Then the force acting on Q2 due to Q1 is along the unit vector As the charge Q2 is unit charge the force exerted onQ2 is nothing but electric field intensity of Q1 at a point where unit charge is placed.

Concept of electric field intensity

 = Q1 / 4 π R²   

If a charge Q1 is located at the centre of the spherical coordinate system then unit vector in equation (3) becomes the radial unit vector coming radially outwards from Q1 and the distance R is the radius of the sphere r.

Electric field due to point charges

Consider n charges Q1,Q2,……..Qn as shown in figure . The combined electric field intensity is to be obtained at point P. The distances of point P from Q1,Q2……Qn are R1,R2,R3………Rn. The unit vectors along these directions are 1, 2, 3……n.

Then the total electric field intensity at point P is the vector sum of the individual field intensities produced by various charges at the point P

 =  +  +  …………………. +

= Q1/ 4 π R²  .     + Q2/ 4 π R²  .   + ……………+ Qn/4 π Rn²  .

1/ 4 π / Ri ² 

Each unit vector can be obtained by using the method discussed earlier

 =   –   / |   –   |

Where  = Position vector of point P

              = Position vector of point where charge Q1 is placed.

Determine the field intensity at P(-0.2,0,0,-2.3) m due to a point charge of +5nC at Q(0.2,0.1,-2.5)m in air.

Substituting value of ,

This is electric field intensity at point P.