Question

An electric dipole consists of charges +q and –q at separation x. At distance d(d >> x) on equatorial position of dipole, the field is proportional to

Answer 1

electric field due to dipole at equatorial line is proportional to x.

It has given that an electric dipole consists of charges +q and -q at seperation x. at distance (d >> x) on equatorial position of dipole, the field is proportional to ....

let a point P is point of observation seperated d distance apart from the midpoint of dipole axis. and also +q is placed at A and -q is placed at B.

now electric field due to +q at a point P, E₁ = kq/[√(d² + x²/4)]² along AP

electric field due to -q at a point P, E₂ = Kq/[√(d² + x²/4)]² along PB

net electric field due to dipole at equatorial line, E = E₁cosΦ + E₂cosΦ

= kq/[√(d² + x²/4)]² × (x/2)/√(d² + x²/4) + kq/[√(d² + x²/4)]² × (x/2)/√(d² + x²/4)

= kqx/(d² + x²/4)³/²

as d >> x so, d² >> x²/4

so, E = kqx/d³

therefore, electric field due to dipole at equatorial line is proportional to x.