Two short electric dipoles are placed in such a manner that their axis coincides and distance between their centres is r. Electric force between these two shart dipoles is found to be proportional `r^(-n)`. What will be the value of n?

Answer

4

Explanation

Electric field on the axis of a short dipole is `E=1/(4piepsilon_0) (2p)/r^3`, Force on an electric dipole placed in electric field which is changing along the axis of dipole is given by `F=p(dE)/(dr)` .
We can write force between electric dipoles in the given situations as follows :
`F=p_1 d/(dr) [1/(4piepsilon_0) (2p_2)/r^3]`
`rArr F=(2p_1p_2)/(4piepsilon_0) d/(dr) [1/r^3] =(2p_1p_2)/(4piepsilon_0) ((-3)/r^4)`
`rArr |F|=(6p_1p_2)/(4piepsilon_0) (r^(-4))`
We can write on comparing that n =4 .