(i) Find potential at point A and B sue to the small charge - system fixed near origin. (Distance between the charges is negligible).
(ii) Find work done to bring a test charge `q_(0)` from point A to point B, slowly. All parameters are in S.I. units.

Explanation

(i) Dipole moment of the system is `vec(P)=(qa) hat(i)+(qa) hat(j)`
Potential at point a due to the dipole
`V_(A)=K ((vec(P).vec(r)))/r^(3)=(K[(qa)hat(i)+(qa)hat(j)]. (4hat(i)+3hat(j)))/5^(3)=(k(qa))/125 (7)`
`implies V_(B)=(K[(qa)hat(i)+(qa)hat(j)](3hat(i)-4hat(j)))/((5)^(3))=(-K (qa))/125`
(ii) `W_(A rarr B)=U_(B)-U_(A)=q_(0) (V_(B)-V_(A))=q_(0) [-(K(qa))/125-((K(qa)(7))/125)]`
`implies W_(A rarr B)=(-Kq q_(0)a)/125 (8)`