Capacitance

If a conducting sphere has its capacitance $1\mu \mathrm{F}$ and electric charge $-10\mathrm{C},$ what is its potential ?

Deduce an expression for the electrostatic energy stored in a capacitor of capacitance $C$ and having charge $Q.$ How will the electric field inside the capacitor be affected when it is completely filled with a dielectric material of dielectric constant ${}^{\text{'}}K^{\text{'}}$?

Deduce an expression for the electrostatic energy stored in a capacitor of capacitance $C$ and having charge $Q.$ How will the energy stored?

Two capacitors of capacitance $C_1$ and $C_2$ having charges $Q_1$ and $Q_2$ are joined together with

positive plate of one connected to the negative plate of the other. Find the common potential in the two cases.

Is the electric field between the two plates uniform? Why guard-ring is used in parallel plate capacitors?

Explain how a capacitor is charged by a cell. Calculate the energy of a charged capacitor. Show that only half of energy expended by a cell is stored up as electrostatic energy. What happens to the other half?

Two spheres of radii $r_1$ and $r_2$ contain charges $Q_1$ and $Q_2$ are situated at a large distance from each other. Now they are joined together by a thin wire. Find surface charge densities of the two. Also find the loss of energy of the two.

Calculate the energy of a charged conductor of capacitance $C$ raised to a potential $V$. How does this energy depend on charge on the conductor?

Can there be a potential difference between two adjacent conductors that carry equal positive charges ?

What is a capacitor? Define capacitance of a capacitor.

Explain why presence of a conductor nearby affects the capacitance of a conductor.

 The dielectric material between the plates of a capacitor 

 $\left(\mathrm{i}\right)$ increases the _____.

Breakdown voltage of a capacitor = dielectric strength of the dielectric medium between the two plates $x$ _____ between the plates.

After charging a capacitor, the battery is disconnected. The gap between the plates is filled by a dielectric slab of dielectric constant $K$ if $C_0,q_0,V_0$ and $u_0$ be the capacitance, charge, potential difference and energy respectively, before introduction, then values after introduction is $C=$_____

An electric field gets within _____ a dielectric medium. If $E_0$ be electric field applied between the plates of capacitor and the dielectric has dielectric constant $k$, then the electric field within the dielectric is $\overrightarrow{E}=\frac{1}{k}$$\overrightarrow{E_0}.$

When a capacitor is charged by connecting it with a cell, the charge it gains is equal to the charge supplied by _____ and the energy it gains is half of the energy spent by the cell.

When charged capacitor is discharged by sparking, the stored energy of a capacitor is converted to heat, sound and _____ energies

When a dielectric of dielectric constant $\mathrm{k}$ is inserted into an air capacitor of capacitance $C_0$, its capacitance becomes _____ times $C_o$.

Removal of a dielectric between the two plates of a charged  capacitor causes _____ of its energy.

 The potential difference between the plates of a charged  parallel plate capacitor increases proportionately with 

$\left(\mathrm{iii}\right)$ the _____  in the distance of separation of the two plates.