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STD 12 - 2. Electric potential and capacitance — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 12 - 2. Electric potential and capacitance4 Marks
MCQ
A dipole having dipole moment $p$ is placed in front of a solid uncharged conducting sphere as shown in the diagram. The net potential at point $A$ lying on the surface of the sphere is :-
  • A
    $\frac{{kp\,\cos \,\phi }}{{{r^2}}}$
  • ✓
    $\frac{{kp\,\cos ^2 \,\phi }}{{{r^2}}}$
  • C
    Zero
  • D
    $\frac{{2kp\,\cos ^2 \,\phi }}{{{r^2}}}$
✓

Answer

Correct option: B.
$\frac{{kp\,\cos ^2 \,\phi }}{{{r^2}}}$
b
In a conductor, potential is same everywhere

$\therefore $ Potential at $\mathrm{A}=$ potential at centre

$=\mathrm{V}_{\text {due to } \mathrm{p}}+\mathrm{V}_{\text {due to induced charges }}$

$=\frac{\mathrm{kp}}{(\mathrm{rsec} \phi)^{2}}+0=\frac{\mathrm{kp} \cos ^{2} \phi}{\mathrm{r}^{2}}$

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