Charges (+q) and (−q) are placed at points A and B, which are 2L ap...

Question

Charges (+q) and (−q) are placed at points A and B, which are 2L apart. C is the midpoint between A and B. What is the work done in moving a charge +Q along the semicircle CRD?

Accepted Answer

📌 Given:
• +q at A, −q at B, separation AB = 2L
• C = midpoint of AB (equatorial point of dipole)
• D = diametrically opposite to C on semicircle

Step 1 — Potential at Point C:
C is equidistant from both charges (distance = L each):
V_C = k(+q)/L + k(−q)/L = 0

Step 2 — Potential at Point D:
D is also equidistant from A and B (by symmetry of semicircle):
V_D = k(+q)/L + k(−q)/L = 0

Step 3 — Work Done:
W = Q × (V_D − V_C) = Q × (0 − 0) = 0

∴ Work done = 0 (Both C and D are at same potential, equipotential points)

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