Electrostatics - Intensity Due To Field Charges

Intensity Due To Field Charges

The electric field intensity at any point due to a group of point charges is equal to the vector sum of the electric field intensities due to individual charges at the same point. For this, we first calculate the electric field intensity at the given point due to individual charges, as if other charges were not there and then add them vectorially i.e.

 
                 

                     (1)

Here, r₁ is the distance of the point P from the ith charge Q₁ and ~r₁ is unit vector directed from Q₁ to the point P.

Now suppose the point charges Q₁, Q₂, Q₃, …. Q_n are located in vacuum at positions 

  respectively. We have to calculate electric field intensity (~E) at any point P where position is ~r. As a net force P is vector sum of the forces due to individual charges, therefore, we can write

 

As   

         (2)

Note that ~E  is a vector quantity that varies from one point to another point in space and its value depends on the positions of the source charges, using polygon law of vectors.

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