Question

show that dipole moment of a dipole is independent of origin​

Answer 1

Answer:

plz mark brainlist

Explanation:

For a system with charge density ρ(r) (which might be volumetric, but which could also include point, line or surface charges by including suitable delta-function terms into ρ(r)), the dipole moment is always defined to be

d=∫rρ(r)dr,

where the integral is taken over all of space. This means that if you displace your origin by r0, then the new dipole moment will be given by

d′=∫r′ρ(r)dr=∫(r−r0)ρ(r)dr=∫rρ(r)dr−r0∫ρ(r)dr=d−r0Q,

i.e. it will change by the product of the coordinate translation and the total charge Q=∫ρ(r)dr of the system. This means that the dipole moment is origin-independent if the system is globally neutral, and it does depend on the coordinate origin if the global charge is nonzero