Question

the force between two short electric dipoles separated by a distance R is directly proportional to​

Answer 1

answer : the force between two short electric dipoles separated by a distance r is directly proportional to 1/r⁴

we know, electric field due to electric dipole at a point r distance from the centre of dipole is...

E ∝ P/r³

we also know force, F = qE

here q = P/r

so, F ∝ P²/r⁴

here P is constant so, F ∝ 1/r⁴

hence, force is directly proportional to 1/r⁴

also read similar questions : electric potential due to a small electric dipole at a large distance r from the centre of the dipole is proportional to

https://brainly.in/question/2512969

The electric potential due to a small electric dipole at a large distance r from the centre of the dipole is proportiona...

https://brainly.in/question/2511842

Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

As you know, electric field due to short diople at an axial position is given by

E = 2Kp/r³

Here P is dipole moment , r is the separation between observation point to middle point of dipole and K is kappa constant.

Now, potential energy of dipole is given by U = -P'EcosФ,

Here Ф is angle between electric field and dipole and p' is dipole moment of other dipole.

∵ dipoles are co-aixal ∴ Ф = 0°

So, U = -P'(2Kp/r³) = -2kpp'/r³

Now, use F = - dU/dr

F = -d{-2kpp'/r³}/dr = 6kpp'/r⁴

Hence, force between two dipole which lies co-axial is inversely proportional to r⁴.