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

Answer: (D)

$\frac{pq}{4\pi\epsilon_0a^2}$

Answer 2

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 tan α =12tan θ , where α =θ +α , and given θ =60∘+α , we can proceed.
Resolving the electric field E into its components:
E cos α =r 34 πϵ 0⋅2 p cos60∘ ⟶ (1)
E sin α =r 34 πϵ 0⋅ p sin60∘ ⟶ (2)
Dividing equation (2) by equation (1):
tan α =12tan _θ and _tan α =tan(θ +α), we find:
α =θ +α by a 2 4 πϵ 0⋅ p ⋅ q
Therefore, the answer is 4 πϵ 0⋅ p ⋅ q.
The correct answer is option (D): $\frac{pq}{4\pi\epsilon_0a^2}$