Q81 / 110 · VITEEE 2023 · Physics

Figure shows three points \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) in a region of uniform electric field \(\vec{E}\). The line \(A B\) is perpendicular and \(\mathrm{BC}\) is parallel to the field lines. Then which of the following holds good? Figure
Where \(\mathrm{V}_{\mathrm{A}}, \mathrm{V}_{\mathrm{B}}\) and \(\mathrm{V}_{\mathrm{C}}\) represent the electric potentials at the points \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) respectively.

  • A
    \(\mathrm{V}_{\mathrm{A}}=\mathrm{V}_{\mathrm{B}}=\mathrm{V}_{\mathrm{C}}\)
  • Correct answer
    B
    \(\mathrm{V}_{\mathrm{A}}=\mathrm{V}_{\mathrm{B}} > \mathrm{V}_{\mathrm{C}}\)
  • C
    \(\mathrm{V}_{\mathrm{A}}=\mathrm{V}_{\mathrm{B}} < \mathrm{V}_{\mathrm{C}}\)
  • D
    \(\mathrm{V}_{\mathrm{A}} > \mathrm{V}_{\mathrm{B}}=\mathrm{V}_{\mathrm{C}}\)

Solution

Here the electric field at A and B is same but at \(\mathrm{C}\) it will decreases, \(\begin{aligned} & \text {so } \mathrm{V}_{\mathrm{A}}=\mathrm{V}_{\mathrm{B}} \\ & \text {and } \mathrm{V}_{\mathrm{C}} \text { is less than } \mathrm{V}_{\mathrm{A}} \text { or } \mathrm{V}_{\mathrm{B}} \\ & \mathrm{V}_{\mathrm{A}}=\mathrm{V}_{\mathrm{B}} > \mathrm{V}_{\mathrm{C}} \end{aligned}\)

Hence, the correct answer is option: 'B'.

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