Question

force between two short electric dipole placed on the same axis at a distance R varies as (1) R^-1 (2)R^-2. choose the correct answer

Answer 1

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.

Answer 2

Answer:

As you know, electric field due to short dipole at an axial position is given by E = 2Kp/r³ =

( C76

4.0

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

Now, potential energy of dipole is given by U Here is angle between electric field and

= -PEcos,

dipole and p' is dipole moment of other dipole.

: dipoles are co-aixal . O = 0° So, U = -P (2Kp/r%) = -2kp/r3

Now, use F = - dU/dr F = -d{-2 kpp'/ryder = 6 kpp'/r*

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