Electric potential and capacitance practice · Mixed difficulty

There is an air filled $1pF$ parallel plate capacitor. When the plate separation is doubled and the space is filled with wax, the capacitance increases to $2pF$. The dielectric constant of wax is

A capacitor is charged by using a battery which is then disconnected. A dielectric slab is then slipped between the plates, which results in

Ten electrons are equally spaced and fixed around a circle of radius $R.$ Relative to $V = 0$ at infinity, the electrostatic potential $V$ and the electric field $E$ at the centre $C$ are

Some charge is being given to a conductor. Then, its potential

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

Statement-II: Potential due to proton is positive.

Two charged conducting spheres of radii $\mathrm{a}$ and $\mathrm{b}$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

A non-conducting ring of radius $0.5\;m$ carries a total charge of $1.11 \times {10^{ - 10}}C$ distributed non-uniformly on its circumference producing an electric field $\vec E$ everywhere in space. The value of the line integral $\int_{l = 0}^{l = \infty } { - \vec E.\overrightarrow {dl} \;(l = 0}$ being centre of the ring) in volt is

A parallel plate capacitor is connected with a battery whose potential difference remains constant . If the plates of the capacitor are shifted apart then the intensity of electric field :

When one electron is taken towards the other electron, then the electric potential energy of the system

The energy stored in a parallel plate capacitor can be treated as the energy of the electric field. The energy per unit volume, due to the electric field is

A cylindrical capacitor has charge $Q$ and length $L.$ If both the charge and length of the capacitor are doubled, by keeping other parameters fixed, the energy stored in the capacitor

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

Given below are two statements.
Statement I : Electric potential is constant within
and at the surface of each conductor.
Statement II : Electric field just outside a charged
conductor is perpendicular to the surface of the
conductor at every point.
In the light of the above statements, choose the
most appropriate answer from the options given
below.

In which form energy is stored in a capacitor:

A sample of $HCl$ gas is placed in an electric field of $3 \times {10^4}\;N{C^{ - 1}}.$ The dipole moment of each $HCl$ molecule is $6 \times {10^{ - 30}}c \times m.$ The maximum torque that can act on a molecule is

The electric potential $V$ at any point $\left( {x,y,z} \right)$, all in meters in space is given by $V = 4{x^2}\;volt.$ The electric field at the point $\left( {1,0,2} \right)$ in $volt/meter$, is

The capacity of a capacitor is 20 F and potential is 5 volts. The charge on the capacitor is

While a capacitor remains connected to a battery and dielectric slab is applied between the plates, then

Assertion (A): Two charges $-q$ each are fixed at points $A$ and $B$. When a third charge $-q$ is moved from $A$ to $B$, electrical potential energy first decreases than increases.

Reason (R) : Along the line joining $A$ and $B$, the third charge is in stable equilibrium position at centre.

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

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

Assertion:- If three capacitors of capacitances $\mathrm{C}_1 < \mathrm{C}_2 < \mathrm{C}_3$ are connected in series and parallel, then $\mathrm{C}_{\text {parallel }} > \mathrm{C}_{\text {series }}$.
Reason:- $\mathrm{C}_{\text {series }}=\mathrm{C}_1+\mathrm{C}_2+\mathrm{C}_3$ and $\frac{1}{\mathrm{C}_{\text {parallel }}}=\frac{1}{\mathrm{C}_1}+\frac{1}{\mathrm{C}_2}+\frac{1}{\mathrm{C}_3}$

Statement-1: If temperature is increased, the dielectric constant of a polar dielectric decreases whereas that of a non-polar dielectric does not change significantly.
Statement-2: The magniude of dipole moment of individual polar molecule decreases significantly with increase in temperature.

When air in a capacitor is replaced by a medium of dielectric constant $K,$ the capacity

A parallel plate capacitor has circular plates of 0.08m radius and $1.0 \times {10^{ - 3}}m$ separation. If a P.D. of $100\;volt$ is applied, the charge will be

Let $V$ be the electric potential at a given point. Then the electric field ${E_x}$ along $x$-direction at that point is given by

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason
R.
Assertion A : Two metallic spheres are charged to the same potential. One of them is hollow and
another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one.
Reason R: Capacitance of metallic spheres depend on the radii of spheres.
In the light of the above statements, choose the correct answer from the options given below:

The energy stored in the condenser is

The electric potential at a point on the axis of an electric dipole depends on the distance $r$ of the point from the dipole as

The condensers of capacity ${C_1}\mathrm{ and }\,\,{C_2}\,$ are connected in parallel, then the equivalent capacitance is: