Three identical positive point charges are located at fixed points in space. Then charge q2q_2 is moved from its initial location to a final location as shown in the figure. Four different paths, marked (a) through (d), are shown. Path (a) follows the phortest line; path (b) takes q2q_2 around q3q_3; path (c) takes q2q_2 around q3q_3 and q1;q_1 ; path (d) takes q2q_2 out to infinity and then to the final location. Which path requires the least work? a) path (a) b) path (b) c) path (c) d) path (d) e) Thework is the same for all the paths.


Answered 1 year ago
Answered 1 year ago
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We will consider that in this physical situation, the electric potential due to a point charge at a distance of rr from the charge is given by

V=k qr\begin{align*} V &= k ~ \dfrac{q}{r} \end{align*}

Therefore, for the system of point charges, the electric potential due to the system is given by

V=k i=1n qiri\begin{align*} V &= k ~ \sum_{i=1}^{n} ~ \dfrac{q_{i}}{r_{i}} \end{align*}

Also, we know that the work done is given by

W=q ΔV=Fd\begin{align*} W &= - q ~ \Delta V \\ \\ &= - F \cdot d \end{align*}

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