electric field due to an electric dipole on its equatorial line | class 12 physics | advguruji

Electric field due to an electric dipole on its -

Consider, an electric dipole of length 2a having charges +q and -q. A point P lies on the equatorial line of the dipole at a distance r from the centre of the dipole. The electric fields due to '-q' and '+q' are E1 and E2 respectively.

Now,

| E1 |  = kq/[(r² + a²)½]²

= kq/(r² + a²)   .....(1)

| E2 |  = kq/[(r² + a²)½]²

= kq/(r² + a²)   .....(2)

From equation (1) and (2)

| E1 |  =  | E2 |  =  x (say)

Clearly, components E1sinθ and E2sinθ cancel each other.

Therefore, Net electric field at point P is -

E = xCosθ + xCosθ

= 2xCosθ

From equation (1)

E = 2kq.Cosθ/(r² + a²)

        = kq2a/[(r² + a²).(r² + a²)½]

  = kq2a/[(r² + a²)³]½

Also, dipole moment -

Questions for Practice

Q1. Find the ratio of electric fields due to a short dipole on the axial line to equatorial line at same distances from the centre.

Ans.   Ea/Ee = (2kp/r³)/(kp/r³)

                  = 2:1

Q2. Find the distance of a point from the centre of a short dipole on the equatorial line such that the net field at that point is 2kV/m. given,

dipole moment = 6 × 10-³ Cm.

Ans.  30 m  (( Do yourself ))

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Electric field due to an electric dipole at any general point

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