Electric potential and capacitance practice · Medium

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

Can a metal be used as a medium for dielectric

An electric dipole is placed making at an angle $60\,^\circ C$ with an electric field of strength $4 \times {10^5}\,\,N/C$. It experiences a torque equal to $8\sqrt 3 \,\,N - m$. Calculate the charge on the dipole, if it is of length 4 cm.

A molecule with a dipole moment $p$ is placed in an electric field of strength E. Initially the dipole is aligned parallel to the field. If the dipole is to be related to be anti-parallel to the field the work required to be done by an external agency is

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

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

Statement-II: Potential due to proton is positive.

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

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

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

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

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 $\frac{1}{\mathrm{C}_{\text {parallel }}}=\frac{1}{\mathrm{C}_1}+\frac{1}{\mathrm{C}_2}+\frac{1}{\mathrm{C}_3}$

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:

Two opposite and equal charges $4 \times {10^{ - 8}}coulomb$ when placed $2 \times {10^{ - 2}}cm$ away, form a dipole. If this dipole is placed in an external electric field $4 \times {10^8}newton/coulomb,$ the value of maximum torque and the work done in rotating in through ${180^\mathrm{o}}$ will be

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

An electric dipole has the magnitude of its charge as $q$ and its dipole moment is $p.$ It is placed in a uniform electric field $E.$ If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively

Equal charges are given to two spheres of different radii. The potential will

Assertion: The electric field due to a dipole on its axis line at a distance $r$ is $E.$ Then, electric field due to the same dipole on the equatorial line and at the same distance will be $E/2.$
Reason: Electric field due to dipole varies inversely as the square of the distance.

A parallel plate capacitor has plate area $A$ and separation $d.$ It is charged to a potential difference ${V_0}.$ The charging battery is disconnected and the plates are pulled apart to three times the initial separation. The work required to separate the plates is