Question

An electric dipole of dipole moment p is placed at the origin of the coordinate system along the z-axis. The amount of work required to move a charge 'q' from the point (a,0,0) to the point (0,0,a) is

• A. \(\frac{pq}{4\pi\epsilon_0a}\)
• B. 0
• C. \(-\frac{pq}{4\pi\epsilon_0a^2}\)
• D. \(\frac{pq}{4\pi\epsilon_0a^2}\)

Answer 1

The Correct Option is D

An electric dipole with a moment p generates an electric field along the x-axis at an angle θ with respect to the x-axis. Using the trigonometric relationship tanα=12tanθ, where α=θ+α, and given θ=60∘+α, we can proceed.
Resolving the electric field E into its components:
Ecosα=r34πϵ0⋅2pcos60∘ ⟶ (1)
Esinα=r34πϵ0⋅psin60∘ ⟶ (2)
Dividing equation (2) by equation (1):
tanα=12tanθ  and tanα=tan(θ+α), we find:
α=θ+α by a2 4πϵ0⋅p⋅q
Therefore, the answer is 4πϵ0⋅p⋅q.
The correct answer is option (D): \(\frac{pq}{4\pi\epsilon_0a^2}\)