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), E → = P → 4 π ϵ 0 r 3, E → = 2 P → 4 π ϵ 0 r 3, E → = - P → 4 π ϵ 0 r 2, E → = - P → 4 π ϵ 0 r 3

MARKS App · Accepted Answer

Use the concept of potential gradient, then the relation, E r = - d V d r ⇒ E θ = - 1 r × d V d θ & V = K P r 2 cos θ , for general point, ⇒ E θ = - 1 r × d K P r 2 cos θ d θ ⇒ E = - K P r 3 1 + 3 cos 2 θ , for the equatorial position, θ = 90 ° ⇒ E → = - k P → r 3 = - P → 4 π ϵ 0 r 3 .

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