Two short electic dipoles of moment P and 8P are placed in opposite direction on a line at a distance of 15cm. The electic will be zero at point between the dipoles wose distance from the dipole of moment P is 

Asked by KRISHPATEL.soc | 20th Jun, 2021, 02:02: PM

Expert Answer:

Electric field E due to a dipole at a distance r far away from its position is given as  
E = K × [ ( 2 p ) / r3 ]
where K = 1/(4πεo ) is Coulomb's constant and p is dipole moment .
Hence electric field of dipole at a far away distance is directly proportional to dipole moment
and  inversely proportional to cube of distance .
As shown in figure, if A is a point which is at a distance r from a dipole of moment P and
at a distance (15-r) from another dipole of moment 8P in opposite direction ,
Then to get zero electric field at A , we have the condition
begin mathsize 14px style 1 over r cubed space minus space 8 over open parentheses 15 minus r close parentheses cubed space equals space 0 space end style
Above expression is simplified as ,  (15 - r ) = 2r   or     r = 5 cm 

Answered by Thiyagarajan K | 20th Jun, 2021, 03:15: PM