As you know, dipole moment is the system of two equal magnitude but just opposite nature charges which are separated small distance.
Here see attachment, dipole is placed along z - axis. and charges q and -q are located in positive z - axis and negative z-axis respectively also distance between charge particle is d .
so, p = qd
A long thread is placed r distance from dipole moment along z - axis.
We know,
electric field due to long thread at r distance from it is given by
E = λ/2π∈₀r
Now, force on q charge by long thread , F₊= E(q) = λq/2π∈₀r i [ positive x-axis ]
force on - q charge by long thread , F₋ = E(-q) = - λq/2π∈₀r i [ negative y - axis ]
∴ net force = F₊ + F₋ = λq/2π∈₀r i - λq/2π∈₀r i = 0
Hence, answer is 0
