In a region of constant potential
In the circuit shown in figure initially key $K_1$ is closed and key $K_2$ is open. Then $K_1$ is opened and $K_2$ is closed (order is important). [Take $Q_1^{\prime}$ and $Q_2^{\prime}$ as charges on $C_1$ and $C_2$ and $V_1$ and $V_2$ as voltage respectively.]
Then,
If a conductor has a potential $V \neq 0$ and there are no charges anywhere else outside, then
A parallel plate capacitor is connected to a battery as shown in figure. Consider two situations.
A. Key $K$ is kept closed and plates of capacitors are moved apart using insulating handle.
B. Key $K$ is opened and plates of capacitors are moved apart using insulating handle.
Choose the correct option(s).
Consider two conducting spheres of radii $R_1$ and $R_2$ with $R_1>R_2$. If the two are at the same potential, the larger sphere has more charge than the smaller sphere. State whether the charge density of the smaller sphere is more or less than that of the larger one.
Since, the two spheres are at the same potential, therefore
$$\frac{k q_1}{R_1}=\frac{k q_2}{R_2} \Rightarrow \frac{k q_1 R_1}{4 \pi R_1^2}=\frac{k q_2 R_2}{4 \pi R_2^2}$$
$$\begin{gathered} \text{or}\quad\sigma_1 R_1=\sigma_2 R_2 \Rightarrow \frac{\sigma_1}{\sigma_2}=\frac{R_2}{R_1} \\ R_2>R_1 \end{gathered}$$
This imply that $\sigma_1>\sigma_2$.
The charge density of the smaller sphere is more than that of the larger one.