Electric potential and capacitance practice · Medium

Consider an electric dipole placed in a region of
non-uniform electric field. Choose the correct
statement out of the following options.

Assertion:- The dipoles in a dielectric are not completely aligned in weak external electric field.
Reason:- Thermal energy tends to de-align them.

Metallic sphere of radius $R$ is charged to potential $V$. Then charge $q$ is proportional to:

Assertion: A metallic shield in form of a hollow shell may be built to block an electric field.

Reason: In a hollow spherical shield, the electric field inside it is zero at every point.

For a polar molecule, which of the following statements is true?

In a Vande graff generator a spherical metal shell is to be a $15 \times {10^5}\,V$ electrode. The dielectric strength of a gas surrounding the electrodes is $5 \times {10^7}\,V{m^{ - 1}}$. The minimum radius of the spherical shell is

A charge of ${10^{ - 9}}C$ is placed on each of the 64 identical drops of radius $2\;cm.$ They are then combined to form a bigger drop. Find its potential

1000 small water drops each of radius $r$ and charge $q$ coalesce together to form one spherical drop. The potential of the big drop is larger than that of the smaller drop by a factor of

Assertion:- A dielectric slab is inserted between the plates of an isolated charged capacitor. The charge on the capacitor will remain the same.
Reason:- Charge on an isolated system is conserved.

If the circumference of a sphere is $3 \mathrm{~m},$ the capacitance of the sphere in water is (dielectric constant of water = 80)

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 ?

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?