Electric potential and capacitance practice · Mixed difficulty

The energy stored in the condenser is

The electric field between the plates of a parallel plate capacitor when connected to a certain battery is ${E_0}.$ If the space between the plates of the capacitor is filled by introducing a material of dielectric constant $K$ without disturbing the battery connections, the field between the plates shall be

When a capacitor is connected to a battery

Two capacitors connected in parallel having the capacities ${C_1}$ and ${C_2}$ are given $'q'$ charge, which is distributed among them. The ratio of the charge on ${C_1}$  and ${C_2}$ will be

An uncharged capacitor is connected to a battery. Show that half the energy supplied by the battery is lost as heat while charging the capacitor.

In an electric field $\mathbf{E}$, the torque acting on a dipole moment $\mathbf{p}$ is

A half ring of radius $R$ has a charge of $\lambda$ per unit length. The potential at the centre of the half ring is $\left( {k = \frac{1}{{4\pi {\varepsilon _0}}}} \right)$

Equipotential surfaces associated with an electric field which is increasing in magnitude along the $x -$ direction are

Dipole is placed parallel to the electric field. If Q is the work done in rotating the dipole by 60°, then work done in rotating it by 180° is

Statement-1: A dielectric is inserted between the plates of an isolated fully-charged capacitor. The dielectric completely fills the space between the plates. The magnitude of electrostatic force on either metal plate decreases, as it was before the insertion of dielectric medium.
Statement-2: Due to insertion of dielectric slab in an isolated parallel plate capacitor (the dielectric completely fills the space between the plates), the electrostatic potential energy of the capacitor decreases.

A test charge is moved from lower potential point to a higher potential point. The potential energy of test charge will:

Two points $P$ and $Q$ are maintained at the potential of $10\;V$ and $- 4V$, respectively. The work done in moving 100 electrons from $P$ to $Q$ is

A parallel plate capacitor is charged. If the plates are pulled apart

If potential (in volts ) in a region is expressed as $V(x,y,z) = 6xy - y + 2yz,$ the electric field ( in N/C) at point (1,1,0) is

Potentiometer measures potential more accurately because

The region surrounding a stationary electric dipole has:

An electric field $E=(20 \hat{i}+25 \hat{j})$ exist in space. If the potential at the origin is zero, then the potential at point $(2 \mathrm{~m}, 4 \mathrm{~m})$ is:

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?

Assertion (A) : From the relation $C=\frac{q}{V}$. We can say that, if more charge $q$ is given to a conductor, its capacitance should increase.

Reason (R) : Ratio $\frac{q}{V}$ will remain constant for a given conductor.

A point charge $+ Q$ is located at a distance of $'r'$ from the centre of an uncharged conducting sphere of radius $R$. The electric potential of that sphere is

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

The electric potential at a point distant $\text{r}$ from an electric dipole is proportional to

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)