Question

In the electric field of a point charge $+q$ placed at point $O$. A charge is carried from point $A$ to $B$ along the diameter and then along the curved path $APB$. Then work done $(OA=OB)$

• A. Along path $APB$ is more
• B. Along path $AB$ is more
• C. Along two paths is equal
• D. Is zero in both cases

Answer 1

The correct option is C Along two paths is equal

Work done by a charge in moving a electric field is given by, when charge moves from $A$ to $B$.

$W=q[V_A-V_B]$

So, In both cases work done depends on the potential of initial point & final point not the distance troweled.

and in both cases, i.e. Path(1) & Path(2),

$U_A=U_B$ because $(OA=OB)$

$\therefore$ The work done along two paths will be equal.

$\Rightarrow$ Option (C) is the correct answer.