Electric potential and capacitance practice · Mixed difficulty

The electric potential at centre of metallic conducting sphere is

Electric intensity due to an electric dipole varies with distance (r ) as $E \propto {r^n},$ where n is

The work done in placing a charge of $5 \times 10^{-18} \mathrm{C}$ on a condenser of capacity $100 \mu \mathrm{F}$ is:

In parallel plate capacitor, electric field between the plate is '$\text{E}$'. If the charge on the plates is '$\text{Q}$' then the force on each plate is

Statement- I: For a charged particle moving from point ${P}$ to point ${Q}$, the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point ${Q}$.

Statement- II: The net work done by a conservative force on an object moving along a closed loop is zero.

In a certain two-dimensional field of force, the potential energy of the particle has the form $U={a} {x}^2+{b} {y}^2,$ where ${a},{b}({a} \neq {b})$ are positive constants with different magnitudes. What is the shape of the equipotential surface for which the magnitude of force vector is constant?

A parallel plate capacitor is charged by
connecting a 2 V battery across it. It is then
disconnected from the battery and a glass slab
is introduced between plates. Which of the
following pairs of quantities decrease?

An equipotential surface and an electric line of force:

Considering a group of positive charges, which of the following statements is correct?

The electric field and the potential of an electric dipole vary with distance ${r}$ as

You have a parallel plate capacitor, a spherical capacitor and cylindrical capacitor. Each capacitor is charged by and then removed from the same battery. Consider the following situations
(i) separation between the plates of parallel plate capacitor is reduced
(ii) radius of the outer spherical shell of the spherical capacitor is increased
(iii) radius of the outer cylinder of cylindrical capacitor is increased
Which of the following is correct ?

A powerful machine used for producing high positive potentials is

Statement-I: In bringing an electron towards a proton electrostatic potential energy of the system increases.

Statement-II: Potential due to proton is positive.

The potentials of the two plates of capacitor are $+ 10V$ and $- 10\;V.$ The charge on one of the plates is $40\;C.$ The capacitance of the capacitor is

Electric potential at any point is $V = - 5x + 3y + \sqrt {15z} ,$ then the magnitude of the electric field is

A parallel plate capacitor with air as dielectric is charged to potential $V$ using a battery. Removing the battery, the charged capacitor is then connected across an identical uncharged parallel plate capacitor filled with wax of dielectric constant $'K'$. The common potential of both the capacitor is

The work done in bringing a 20 coulomb charge from point $A$ to point $B$ for distance 0.2 m is 2 joule. The potential difference between the two points will be (in volt)

The capacity of a parallel plate capacitor increases with the

If we move opposite direction of electric field then electric potential

Two concentric hollow spherical shells have radii $\text{r}$ and $\text{R} (\gg \text{r}).$ A charge $\text{Q}$ is distributed on them such that the surface charge densities are equal. The electric potential at the centre is

Which of the following statements about dipole moment is not true?

If the distance between the plates of a capacitor is $\mathrm{d}$ and potential difference is $\mathrm{V}$ then what is the energy density between the plates?

A capacitor of unknown capacitance $\mathrm{C}$ is connected across a battery of $\text{V}$ volt. The charge stored in it becomes $\text{Q}$ coulomb. When potential across the capacitor is reduced by $\text{V}^{\prime}$ volt, the charge stored in it becomes $\text{Q}^{\prime}$ coulomb. The capacitance $\text{C}$ is

Assertion (A): Electric potential on the surface of a charged sphere of radius $R$ is $V$. Then electric field at a distance $r=\frac{R}{2}$ from centre is $\frac{V}{2 R}$. Charge is distributed uniformly over the volume.

Reason (R) : From centre to surface, electric field varies linearly with $r$. Here, $r$ is distance from centre.

If combining two charged bodies, the current does not flow then

The plates in a parallel plate capacitor are separated by a distance $d$ with air as the medium in between the plates. In order to increase the capacity by 66 %, a dielectric slab of dielectric constant 5 is introduced in between the plates. The thick ness of the dielectric slab required is

Consider the fusion in helium plasma. Find the temperature at which the average thermal energy $1.5 \mathrm{~kT}$ equals the Coulomb potential energy at $2 \mathrm{~fm}$.

Assertion (A) : If we see along the axis of a charged ring, the magnitude of electric field is minimum at centre and magnitude of electric potential is maximum.

Reason (R): Electric field is a vector quantity while electric potential is scalar.

The kinetic energy of a charged particle decreases by $10 \mathrm{~J}$ as it moves from a point at potential $100 \mathrm{~V}$ to a point at potential $200 \mathrm{~V}$. Find the charge on the particle.

If $E$ is the electric field intensity of an electrostatic field, then the electrostatic energy density is proportional to