In the following diagram, the work done in moving a point charge from point P to point $\mathrm{A},…

In the following diagram, the work done in moving a point charge from point P to point $\mathrm{A}, \mathrm{B}$ and C are $\mathrm{W}_{\mathrm{A}}, \mathrm{W}_{\mathrm{B}}$ and $\mathrm{W}_{\mathrm{C}}$ respectively. Then (A, B, C are points on semicircle and point charge $q$ is at the centre of semicircle)
  1. $\mathrm{W}_{\mathrm{A}}=\mathrm{W}_{\mathrm{B}}=\mathrm{W}_{\mathrm{C}} \neq 0$
  2. $\mathrm{W}_{\mathrm{A}}=\mathrm{W}_{\mathrm{B}}=\mathrm{W}_{\mathrm{C}}=0$
  3. $\mathrm{W}_{\mathrm{A}}\gt\mathrm{W}_{\mathrm{B}}\gt\mathrm{W}_{\mathrm{C}}$
  4. $\mathrm{W}_{\mathrm{A}} \lt \mathrm{W}_{\mathrm{B}} \lt \mathrm{W}_{\mathrm{C}}$

Solution

As points $\mathrm{A}, \mathrm{B}$ and C lie on semicircle, $\begin{array}{ll}\therefore & V_A=V_B=V_C=V \\ \therefore & W_A=q\left(V_A-V_P\right)=q\left(V-V_P\right) \\ & W_B=q\left(V_B-V_P\right)=q\left(V-V_P\right) \\ & W_C=q\left(V_C-V_P\right)=q\left(V-V_P\right) \\ \therefore & W_A=W_B=W_C \neq 0\end{array}$

Asked in: AP EAMCET 2024 (19 May Shift 2)

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