Electric field intensity due to a point charge/group of charges

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.

1.png

Then force on charge q due to point charge Q is given by
daum_equation_1434388710099.png

Therefore,electric field intensity at point P due to point charge Q is given by

daum_equation_1434389004951.png
or

daum_equation_1434392495384.png

**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:
  1. If the charges are present in air than ϵ is replaced by ϵo (since ϵ = ϵrϵo and for air ϵr = 1).
  2. When source charge is away from origin O,then electric field due to charge Q at point P is given by

2.png
daum_equation_1434392324149.png

Electric field intensity due to a group of charges
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).

3.png

Then,electric fields due to point charges q1, q2,q3, qn at point P are given by,

daum_equation_1434391924487.png

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

daum_equation_1434391799451.png

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