The electric field at a point on the equatorial plane at a distance r from the centre of a dipole having dipole moment p → is given by ( r separation of two charges forming the dipole, ϵ 0 - permittivity of free space)

Question

The electric field at a point on the equatorial plane at a distance r from the centre of a dipole having dipole moment p → is given by ( r > > separation of two charges forming the dipole, ϵ 0 - permittivity of free space)

Aicharya · Accepted Answer

Use the concept of potential gradient, then the relation,

E_{r} = - \frac{d V}{d r} \Rightarrow E_{θ} = - \frac{1}{r} \times \frac{d V}{d θ} & V = \frac{K P}{r^{2}} \cos θ

, for general point,

\Rightarrow E_{θ} = - \frac{1}{r} \times \frac{d (\frac{K P}{r^{2}} \cos θ)}{d θ} \Rightarrow E = - \frac{K P}{r^{3}} \sqrt{1 + 3 \cos^{2} θ}

, for the equatorial position,

θ = 90 °

The electric field at a point on the equatorial plane at a distance r from the centre of a dipole having…

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