Electric potential and capacitance practice · Mixed difficulty

A parallel plate capacitor is filled with a dielectric whose dimensions are the same as that of the capacitor. The capacitor is connected to a battery.
Statement 1: If the dielectric is pulled out, the electric field inside the capacitor increases.
Statement 2: The electric field inside the dielectric is lesser than the electric field in the region outside the dielectric.

Statement-1: A parallel plate capacitor is charged to a potential difference of $100 \mathrm{~V}$, and disconnected from the voltage source. A slab of dielectric is then slowly inserted between the plates. Compared to the energy before the slab was inserted, the energy stored in the capacitor with the dielectric is decreased.
Statement-2: When we insert a dielectric between the plates of a capacitor, the induced charges tend to draw in the dielectric into the field (just as neutral objects are attracted by charged objects due to induction). We resist this force while slowly inserting the dielectric, and thus do negative work on the system, removing electrostatic energy from the system.

An electric dipole of moment ${\vec p}$ placed in a uniform electric field ${\vec E}$ has minimum potential energy when the angle between ${\vec p}$ and ${\vec E}$ is

A capacitor has air as dielectric medium and two conducting plates of area $12 \mathrm{~cm}^2$ and they are $0.6 \mathrm{~cm}$ apart. When a slab of dielectric having area $12 \mathrm{~cm}^2$ and $0.6 \mathrm{~cm}$ thickness is inserted between the plates, one of the conducting plates has to be moved by $0.2 \mathrm{~cm}$ to keep the capacitance same as in previous case. The dielectric constant of the slab is: $\left(\text{Given }\varepsilon_0=8.834 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right)$

Assertion:- Two adjacent conductors carrying the same charge can be at different potentials.
Reason:- The conductors may have different sizes and hence different capacitances.

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

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.

An air capacitor is charged with an amount of charge $q$ and dipped into an oil tank. If the oil is pumped out, the electric field between the plates of capacitor will

A parallel plate condenser with oil between the plates (dielectric constant of oil $K = 2$) has a capacitance $C.$ If the oil is removed, then capacitance of the capacitor becomes

The electric potential $V$ at any point $(x, y, z)$ in space is given according to relation $V=2 x^2 {V}$. The electric field intensity at the point $(2 \mathrm{m}, 0,2 \mathrm{m})$ will be $-E$ (volt/metre) then the value of $E$ is

A capacitor is kept connected to the battery and a dielectric slab is inserted between the plates. During this process

A parallel plate capacitor of plate area $A$ and plate separation $d$ is charged to potential $V$ and then the battery is disconnected. A slab of dielectric constant $k$ is then inserted between the plates of the capacitors so as to fill the space between the plates. If $Q,E$ and $W$ denote respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted) and work done on the system in question in the process of inserting the slab, then state incorrect relation from the following

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

One volt is equivalent to:

$N$ identical spherical drops charged to the same potential $V$ are combined to form a big drop. The potential of the new drop will be

A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A. If the rate of change of potential difference between the plates is $7 \times 10^8 \mathrm{V} / \mathrm{s}$ then the integer value of the distance between the parallel plates is ____ $\mu \mathrm{m}.$

$\left(\text{Take }\epsilon_0=9 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}, \pi=\frac{22}{7}\right)$

A capacitor of capacitance $9 \mathrm{~nF}$ having dielectric slab of ${\varepsilon _r}=2.4,$ dielectric strength $20 \mathrm{~MV} / \mathrm{m}$ and $P.D. = 20 \mathrm{~V}$ calculate area of plates.

Statement-I: Due to two point charges electric field and electric potential can't be zero at some point simultaneously.
Statement-II: Field is a vector quantity and potential a scalar quantity.

A parallel plate capacitor having a plate separation of $2mm$ is charged by connecting it to a $300V$ supply. The energy density is

When a positive $q$ charge is taken from lower potential to a higher potential point, then its potential energy will

An electric dipole in a uniform electric field experiences (When it is placed at an angle $\theta$ with the field)

Two charges are at a distance $'d'$ apart. If a copper plate (conducting medium) of thickness $\frac{d}{2}$ is placed between them, the effective force will be

Assertion (A) : Two capacitors are connected in series with a battery. Energy stored across them is in inverse ratio of their capacity.

Reason (R): $U=\frac{1}{2} q V$ or $U \propto q V$.

Assertion (A) : A small electric dipole is moved translationally from higher potential to lower potential in uniform electric field. Work done by electric field is positive.

Reason (R) : When a positive charge is moved from higher potential to lower potential, work done by electric field is positive.

The work done in bringing a unit positive charge from infinite distance to a point at distance $x$ from a positive charge $Q$ is $W.$ Then the potential $\phi$ at that point is

A body of capacity $4\;\mu \;F$ is charged to $80\;V$ and another body of capacity $6\mu \;F$ is charged to $30V.$ When they are connected the energy lost by $4\mu \;F$ capacitor is

A large insulated sphere of radius $r$ charged with $Q$ units of electricity is placed in contact with a small insulated uncharged sphere of radius $r^{\prime}$ and in then separated. The charge on smaller sphere will now be

The capacity of a parallel plate capacitor increases with the

A capacitor of capacity $C$ has charge $Q$ and stored energy is $W$. If the charge is increased to $2Q$, the stored energy will be

A system consists of four equal charges - $\mathrm{Q}$ placed at the four corners of a square and another charge $\mathrm{q}$ is placed at the centre of the square, then the value of $\mathrm{q}$ for which the system is equilibrium, is