Initial charge stored $=50\mu\text{c}$
Let the dielectric constant of the material induced be ‘k’.
Now, when the extra charge flown through battery is 100.
So, net charge stored in capacitor $=150\mu\text{c}$
Now, $\text{C}_1=\frac{\in_0\text{A}}{\text{d}}$ or $\frac{\text{q}_1}{\text{V}}=\frac{\in_0\text{A}}{\text{d}}\ \dots(1)$
$\text{C}_2=\frac{\in_0\text{Ak}}{\text{d}}$ or $\frac{\text{q}_2}{\text{V}}=\frac{\in_0\text{Ak}}{\text{d}}\ \dots(2)$
Dividing (1) and (2) we get $\frac{\text{q}_1}{\text{q}_2}=\frac{1}{\text{k}}$
$\Rightarrow\frac{50}{150}=\frac{1}{\text{k}}$
$\Rightarrow\text{k}=3$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
OR
A thin conducting spherical shell of radius R has charge Q spread uniformly over its surface. Using Gauss’s theorem, derive an expression for the electric field at a point outside the shell.
Draw a graph of electric field E(r) with distance r from the centre of the shell for
$0\leq\text{r}\le\infty.$OR
Find the electric field intensity due to a uniformly charged spherical shell at a point (i) outside the shell and (ii) inside the shell. Plot the graph of electric field with distance from the centre of the shell.
OR
Using Gauss’s law obtain the expression for the electric field due to a uniformly charged thin spherical shell of radius R at a point outside the shell. Draw a graph showing the variation of electric field with r, for r > R and r < R.
