# Electric Field at an Equatorial Point of a Dipole | cbse24.com

### The electric field at an equatorial point of a dipole:

As shown in fig consider an electric dipole consisting of charges -q and +q, separated by distance 2a and placed in a vacuum. Let P be a point on the equatorial line of the dipole at distance r from it.

i.e.    OP=r The electric field at an equatorial point of a dipole

By geometry ∠PAO = ∠RPA     (∴ PR ॥ AO)
and ∠PBO = ∠ MPR Simulation of Electric field at an Equatorial point of a dipole

The electric field at point P due to +q charge is

E+q

=14πϵ0.qr2+a2)(√
2
=14πϵ0.q            ,direction along BPr2+a2

The electric field at point P due to -Q charge is

Eq

=14πϵ0.qr2+a2)(√
2
=14πϵ0.q           ,direction along PAr2+a2

Thus the magnitudes of E+q and E-q are equal  i.e.

Eq=E+q=14πϵ0.qa2+r2
E    E+q
Clearly, the normal components of E-q and E+q will cancel out. The horizontal component or parallel components to the dipole axis add up. The total electric field Eequa   is opposite to p⃗

Eequa=(Eqcosθ+E+qcosθ).p ^

=2Eqcosθp^

=2.14πϵ0qa2+r2.aa2+r2p^                   [∴cosθ=aa2+r2]

Eequa=14πϵ0.p(a2+r2)3/2p^

Where p=2qa, is the electric dipole moment.

If the point p is located far away from the dipole,

r>>a, then

Eequa=14πϵ0.pr3p^

Clearly, the direction of the electric field at any point on the equatorial line of the dipole will be antiparallel to the dipole moment p⃗

### Comparison of an electric field of dipole at axial and equatorial points.

Eaxial=2Eequatorial

the electric field of a short dipole at a distance r along its axis is twice the electric field at the same distance along the equatorial line.

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