Electric potential and capacitance practice · Mixed difficulty

A conductor which can be given almost unlimited charge is_____.

Eight identical spherical drops, each carrying a charge $1 \mathrm{nC}$ are at a potential of $900 \mathrm{~V}$ each. All these drops combine together to form a single large drop. Calculate the potential of this large drop. (Assume no wastage of any kind and take the capacitance of a sphere of radius $r$ as proportional to $r$ ).

A capacitor $4\mu F$ charged to $50V$ is connected to another capacitor of $2\mu F$ charged to $100V$ with plates of like charges connected together. The total energy before and after connection in multiples of $\left( {{{10}^{ - 2}}J} \right)$ is

A positive point charge $+\mathrm{q}$ is placed at the origin. There is an electric field $E_{(x)}=E_0\left(2 \frac{x}{d}+3 \frac{x^2}{d^2}\right)$, that accelerates the point charge along the $\mathrm{x}$-axis. The kinetic energy of the charge when it reaches the position $\mathrm{x}=2 \mathrm{~d}$ is $X q d E_0$ then find the value of $X$.

A capacitor of capacitance $1 \mu F$ can with stand the maximum voltage $6 \mathrm{kV}$ while a capacitor of $2 \mu \mathrm{F}$ can withstand the maximum voltage $4 \mathrm{kV}$. What maximum voltage (in $\mathrm{kV})$ will the system of these two capacitor can withstand, if they are connected in series?

A short electric dipole is placed in the electric field due to a point charge. Then

A) The dipole must experience a force

B) The dipole may experience a force

C) The dipole must experience a torque

D) The dipole may experience a torque

Polar molecules are the molecules

Assertion: Two equipotential surfaces can cut each other.

Reason: Two equipotential surfaces are always parallel to each other.

The force between two short dipoles separated by a distance $r$ is directly proportional to

Assertion (A): Two capacitor of same capacity are connected first in parallel and then in series. The ratio of resultant capacities in the two cased will be $4: 1.$

Reason (R): In parallel, capacity increases and in series capacity decreases.

Assertion (A): Conductors having equal positive charge and volume, must also have same potential.
Reason (R): Potential depends only on charge and volume of conductor.

The capacitance of two conductors in parallel is four times when they are connected in series. The ratio of the individual capacitance will be

Two conducting spheres of radii $R_1$ and $R_2$ are kept widely separated from each other. What are their individual capacitances? If the spheres are connected by a metal wire, what will be the capacitance of the combination? Think in terms of series-parallel connections.

An electric field is expressed as $E=2 \hat{i}+3 \hat{j}$. Find the potential difference $\left(V_A-V_B\right)$ between two points $A$ and $B$ whose position vectors are given by $r_A=\hat{i}+2 \hat{j}$ and $r_B=2 \hat{i}+\hat{j}+3 \hat{k}$.

Two identical capacitors have same capacitance $C$. One of them is charged to the potential $V$ and other to the potential $2 V$. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is:

The intensity of electric field at a point between the plates of a charged capacitor

A parallel-plate capacitor of capacitance $100 \mu \mathrm{F}$ is connected to a power supply of $200 \mathrm{~V}$. A dielectric slab of dielectric constant 5 is now inserted into the gap between the plates. (a) Find the extra charge flown through the power supply and the work done by the supply. (b) Find the change in the electrostatic energy of the electric field in the capacitor.

A hollow spherical conductor of radius $r$ and potential of $100 \mathrm{~V}$ at its outer surface. The potential inside the hollow at a distance of $r / 2$ from its centre is

A parallel plate capacitor has capacitance of $2\mu F$ in air and $12\mu F$ when immersed in oil. The dielectric constant of oil

A hollow metallic sphere of radius $R$ is given a charge $Q$. Then, the potential at the centre is

An electric dipole having dipole moment $4 \times$ $10^{-9} \mathrm{Cm}$ makes an angle $30^{\circ}$ with the direction of a uniform electric field of magnitude 5 $\times 10^4 \mathrm{NC}^{-1}$. Calculate the magnitude of the torque acting on the dipole. Also find out work required to rotate the dipole to make angle $90^{\circ}$ with the direction of the electric field.

Assertion: A parallel plate capacitor is connected across battery through a key. A dielectric slab of dielectric constant ${k}$ is introduced between the plates. The energy stored becomes ${k}$ times.
Reason: The surface density of charge on the plate remains constant.

The ratio of charge densities on the surface of two conducting spheres is 3 : 2 If the radii of the spheres are 4 cm and 8 cm. the ratio of electric potential on the surfaces of the spheres is

There is an electric field $E$ in $X -$direction. If the work done on moving a charge $0.2\;C$ through a distance of $2\;m$ along a line making an angle $60^\circ$ with the $X -$axis is $4.0$, what is the value of $E$

An electric dipole is made up of two equal and opposite charges of $2 \times 10^{-6} {C}$ at a distance of $3 {~cm}$. If this is kept in an electric field of $2 \times 10^5$ ${N} / {C}$, then the maximum torque acting on the dipole is

The energy stored in a capacitor of capacitance $\text{C}$ having a charge $\text{Q}$ under a potential $\text{V}$ is

Electron and proton is moving away from each other then potential energy of system

The electric potential due to a small electric dipole at a large distance $r$ from the centre of the dipole is proportional to

The angle between the dipole moment and electric field at any point on the equatorial plane is:

It becomes possible to define potential at a point in an electric field because electric field: