A point charge q moves from point P to point | vedclass

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Question

(B) The electric field is a conservative field,so the work done by the electric field depends only on the initial and final positions,not on the path

Vedclass · Accepted Answer

$-qEa$

Vedclass · Answer

(B) The electric field is a conservative field,so the work done by the electric field depends only on the initial and final positions,not on the path taken.Work done $W = \vec{F} \cdot \vec{d} = q\vec{E} \cdot \vec{d}$,where $\vec{d}$ is the displacement vector.The initial position is $P(a, b, 0)$ and the final position is $S(0, 0, 0)$.The displacement vector $\vec{d} = \vec{S} - \vec{P} = (0 - a)\hat{i} + (0 - b)\hat{j} + (0 - 0)\hat{k} = -a\hat{i} - b\hat{j}$.The electric field is $\vec{E} = E\hat{i}$.Work done $W = q(E\hat{i}) \cdot (-a\hat{i} - b\hat{j}) = qE(-a) = -qEa$.

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