The potential of the centre of a hollow charged spherical conductor is 1000 V. If the radius of the sphere is 10 cm, then charge on the sphere is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 0.011\,\mu\mathrm{C} \)
Inside a charged conductor the field is zero, so the potential is constant throughout the inside and equal to the potential on the surface.
\( \displaystyle V_{\mathrm{centre}} = V_{\mathrm{surface}} = \frac{q}{4\pi\varepsilon_0 R} \)
\( \displaystyle q = 4\pi\varepsilon_0 R V = \frac{R V}{9\times10^{9}} \)
\( R = 10\,\mathrm{cm} = 0.1\,\mathrm{m} \)
\( V = 1000\,\mathrm{V} \)
\( \displaystyle q = \frac{0.1 \times 1000}{9\times10^{9}} = 1.1\times10^{-8}\,\mathrm{C} = 0.011\,\mu\mathrm{C} \)