Electric field intensity due to a point charge
Consider a fixed point charge Q at the origin O.Let q be the test charge placed in a medium at a distance r from origin in the electric field of the charge Q.
Then force on charge q due to point charge Q is given by
Therefore,electric field intensity at point P due to point charge Q is given by
or
**This shows that the electric intensity due to a point charge is directly proportional to the magnitude of charge Q and inversely proportional to the square of distance.
Note:
  Electric field intensity due to a group of charges
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Consider a system of charges q1, q2,q3 …, qn placed at a distance r1,r2,r3 …, rn relative to some origin O.Let q be the test charge at point P where the total electric field due to n charges is to be determined..Let test charge q placed in a medium at a distance r from origin (i.e. at point P).
Then,electric fields due to point charges q1, q2,q3 …, qn at point P are given by,
Now applying principle of superposition which says that net electric field strength at a point due to a group of charges is equal to the vector sum of all the electric field strengths produced due to individual charges at that point.
Therefore,net electric field at point P is given by
