Question

Charges + q and – q are placed at point A and B respectively which are a distance 2L apart, C is the midpoint between A and B. The work done in moving a charge + Q along the semicircle CRD is……. 

(A) [(qQ)/(2π∈₀L)] 

(B) [(– qQ)/(6π∈₀L)] 

(C) [(qQ)/(6π∈₀L)] 

(D) [(qQ)/(4π∈₀L)]

Answer 1

The correct option (B) [(– qQ)/(6π∈₀L)]

Explanation:

from given data, 

AC = L

BC = L

BD = L

Work done in moving + Q along CRD = W &

W = Q(V_D – V_C) (1)

Now V_C = k[(q/L) – (q/L)] = 0

V_D = k[{q/(L + L + L)} + {(– q)/L}] = k[(q/3L) – (q/L)] = [(– 2qk)/(3L)]

from (1), W = Q[(– 2qk)/(3L)]

put k = [1/(4π∈₀)] hence W = (– qQ) [(2 × 1)/(4π∈₀ × 3L)]

= [(– qQ)/(6π∈₀L)]