Charges +q and -q are placed at points 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

Question

Charges +q and -q are placed at points 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 /2 π ∈ 0 L ) (B) ( qQ /6 π ∈ 0 L ) (C) -( qQ /6 π ∈0 L ) (D) ( qQ /4 π ∈0 L )

Tardigrade Admin · Accepted Answer

W =Δ U = Q ( V D - V C ) here V C =0 = Q [( q /4 π ϵ0 (3 L ))-( q /4 π ∈0 ( L ))-0]=(- Qq /6 π ∈0 L )

Q. Charges $+ q$ and $- q$ are placed at points $A$ and $B$ respectively which are a distance $2 L$ apart, $C$ is the midpoint between $A$ and $B$ . The work done in moving a charge $+ Q$ along the semicircle $CR D$ is

$\frac{qQ}{2 π \in _{0} L}$

$\frac{qQ}{6 π \in _{0} L}$

$- \frac{qQ}{6 π \in _{0} L}$

$\frac{qQ}{4 π \in _{0} L}$

$W = Δ U = Q (V_{D} - V_{C})$ here $V_{C} = 0$
$= Q [\frac{q}{4 π ϵ _{0} ( 3 L )} - \frac{q}{4 π \in _{0} ( L )} - 0] = \frac{- Qq}{6 π \in _{0} L}$

Q. Charges +q and −q are placed at points 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

2π∈0​LqQ​

6π∈0​LqQ​

−6π∈0​LqQ​

4π∈0​LqQ​