CBSE Class 12-science Answered

In this case we determine the electric field at a point P which is located on the perpendicular bisector of the line joining the two charges. Let the distance of P from this line be y.

Magnitude of electric field at P due to – q:

 is directed from P to A. It has vertical component directed in the -y direction, and a horizontal component directed in the – x direction.

Magnitude of E at P due to + q:

 is directed from B to P. It has vertical component directed in the +y direction, and a horizontal component directed in the – x direction.

 The net electric field at P is calculated by adding vectorially  and .

As their vertical components,  and , are equal in magnitude but opposite in direction.  Hence they cancel out.

And, the horizontal components are both in the –x direction. Hence they add up.

Thus,

From simple trigonometry, where we can substitute cos θ in terms of a and y, we get                                                                                                                                                                                   
     

For, neglect  in the denominator.

Thus, we get

But the dipole moment of an electric dipole is

Hence, for a point P at a very large perpendicular distance from the axis,

                     (for )