CBSE 2024 · Region 3 · Set 3 · Q31 · 5 marks
(i)Obtain the expression for the capacitance of a parallel plate capacitor with a dielectric medium between its plates.(ii)A charge of $\displaystyle 6 \mu \mathrm{C}$ is given to a hollow metallic sphere of radius $\displaystyle 0.2$ m . Find the potential at (i) the surface and (ii) the centre of the sphere.
(i)
Obtain the expression for the capacitance of a parallel plate capacitor with a dielectric medium between its plates.
(ii)
A charge of $\displaystyle 6 \mu \mathrm{C}$ is given to a hollow metallic sphere of radius $\displaystyle 0.2$ m . Find the potential at (i) the surface and (ii) the centre of the sphere.
Marking-scheme solution
(i)
at the surface &
(ii)
at the centre &
When a dielectric slab is inserted between the plates of capacitance there is induced charge density \(\displaystyle \sigma_{\mathrm{P}}\) which opposes the original charge density \(\displaystyle (\sigma)\) on the plate of capacitance.
Electric field with dielectric medium is
\[\begin{aligned}
& \mathrm{E}=\frac{\left(\sigma-\sigma_{\mathrm{P}}\right)}{\varepsilon_{0}} \\
& \mathrm{~V}=\mathrm{E} \times \mathrm{d}=\frac{\left(\sigma-\sigma_{\mathrm{P}}\right)}{\varepsilon_{0}} \mathrm{d}
\end{aligned}
\]
\[\left(\sigma-\sigma_{\mathrm{P}}\right)=\frac{\sigma}{\mathrm{K}}
\]
\[\mathrm{V}=\frac{\sigma \mathrm{d}}{\varepsilon_{0} \mathrm{K}}=\frac{\mathrm{Qd}}{\mathrm{~A} \varepsilon_{0} \mathrm{K}}
\]
\[\mathrm{C}=\frac{Q}{\mathrm{V}}=\frac{\mathrm{K} \varepsilon_{0} A}{\mathrm{d}}
\]
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CBSE Class 12 Physics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.