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Physics Question on Electric Dipole

In the situation shown in the diagram, magnitude of q << | Q | and r>>a. The net force on the free charge -q and net torque on it about O at the instant shown are respectively
[ p = 2aQ is the dipole moment ]
diagram of particles and free charge and net torque

A

14πϵ0pqr2k^,14πϵ0pqr3i^\frac{1}{4\pi\epsilon_0}\frac{pq}{r^2}\hat{k},\frac{1}{4\pi\epsilon_0}\frac{pq}{r^3}\hat{i}

B

−14πϵ0pqr2k^,−14πϵ0pqr3i^-\frac{1}{4\pi\epsilon_0}\frac{pq}{r^2}\hat{k},-\frac{1}{4\pi\epsilon_0}\frac{pq}{r^3}\hat{i}

C

14πϵ0pqr3i^,+14πϵ0pqr2k^\frac{1}{4\pi\epsilon_0}\frac{pq}{r^3}\hat{i},+\frac{1}{4\pi\epsilon_0}\frac{pq}{r^2}\hat{k}

D

14πϵ0pqr3i^,−14πϵ0pqr2k^\frac{1}{4\pi\epsilon_0}\frac{pq}{r^3}\hat{i},-\frac{1}{4\pi\epsilon_0}\frac{pq}{r^2}\hat{k}

Answer

14πϵ0pqr3i^,−14πϵ0pqr2k^\frac{1}{4\pi\epsilon_0}\frac{pq}{r^3}\hat{i},-\frac{1}{4\pi\epsilon_0}\frac{pq}{r^2}\hat{k}

Explanation

Solution

The correct answer is (D) : 14πϵ0pqr3i^,−14πϵ0pqr2k^\frac{1}{4\pi\epsilon_0}\frac{pq}{r^3}\hat{i},-\frac{1}{4\pi\epsilon_0}\frac{pq}{r^2}\hat{k}.