Electric potential and capacitance practice · Mixed difficulty

Which of the following is not true?

A point charge $q$ is rotated along a circle in the electric field generated by another point charge $Q.$ The work done by the electric field on the rotating charge in one complete revolution is

A hollow metal sphere of radius $5 \mathrm{~cm}$ is charged such that the potential on its surface is $10 \mathrm{~V}$. The potential at the centre of the sphere is

When an electric dipole $\mathbf{p}$ is placed in a uniform electric field $\mathbf{E}$, then at what angle between $\mathbf{p}$ and $E$ the value of torque will be maximum?

If a dielectric substance is introduced between the plates of a charged air-gap capacitor. The energy of the capacitor will

If a positive charge is shifted from a low-potential region to a high-potential region, then energy is

Four charges $+Q,-Q,+Q$ and $-Q$ are situated at the corners of a square; in a sequence then at the centre of the square

Two charged particles, having equal charges of $2.0 \times 10^{-5} \mathrm{C}$ each, are brought from infinity to within a separation of $10 \mathrm{~cm}$. Find the increase in the electric potential energy during the process.

One micro microfarad is equal to

The capacitance of an isolated conducting sphere of radius $R$ is proportional to

Three capacitors of $2\mu F,\;3\mu F$ and $6\mu F$ are joined in series and the combination is charged by means of a $24\;volt$ battery. The potential difference between the plates of the $6\mu F$ capacitor is

Three concentric spherical shells have radii a, b and $\mathrm{c}(\mathrm{a} < \mathrm{b} < \mathrm{c})$ and have surface charge densities $\sigma,-\sigma$ and $\sigma$ respectively. If $V_A, V_B$ and $\mathrm{V}_{\mathrm{C}}$ denote the potentials of the three shells, then, for $V_A=V_C$, we get -

Two charges +q and –$q$ are kept apart. Then at any point on the right bisector of line joining the two charges

The displacement of a charge $Q$ in the electric field $\vec E = {e_1}\hat i + {e_2}\hat j + {e_3}\hat k$ is $\vec r = a\hat i + b\hat j$. The work done is

Two spheres of radii $r$ and $R$ carry charges $q$ and $Q$ respectively. When they are connected by a wire, there will be no loss of energy of the system if

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)

Three charges each $20\mu C$ are placed at the corners of an equilateral triangle of side $0.4m$. The potential energy of the systems is…… $J$

Two square plates are at potential difference of 100 V separated by 2 cm. calculate electric intensity between them.

The electric field at a point on the equatorial plane at a distance $\text{r}$ from the centre of a dipole having dipole moment $\text{P}$ is given by $(\text{r} \gg$ separation of two charges forming the dipole, $\varepsilon_0$= permittivity of free space)

A capacitor has capacitance $2 \mathrm{~F}$. plate separation $0.5 \mathrm{~cm}$ then area of plate

On moving a charge of 30 coulombs by 3 cm, 6 J of work is done, then the potential difference between the points is

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

An insulated charged sphere of radius 5 cm has
a potential of 10 V at the surface. The potential
at centre will be

If $20 \mathrm{~J}$ of work has to be done to move an electric charge of $4 \mathrm{C}$ from a point, where potential is $10 \mathrm{~V}$ to another point, where potential is $\mathrm{V}$, find the value of $\mathrm{V}$.

A $4\,\,\mu F$ conductor is charged to $\mathrm{400}\,\,\mathrm{V}$ and then its plates are joined through a resistance of $\mathrm{1}\,\,\mathrm{K\Omega }$. The heat produced in the resistance is

A solid sphere of radius $\mathrm{R}$ is charged uniformly. At what distance from its surface is the electrostatic potential half of the potential at the centre

The relation between the intensity of the electric field of an electric dipole at a distance r from its centre on its axis and the distance r is where ($r \gg 2l)$

If 7 charge $q$ are placed at corners of cube of edge length $\sqrt{3} \mathrm{~m}$ then find potential at centre of cube:

Which one statement is correct? A parallel plate air condenser is connected with a battery. Its charge, potential, electric field and energy are $Q_0, V_0, E_0$ and $U_0$ respectively. In order to fill the complete space between the plates a dielectric slab is inserted, the battery is still connected. Now the corresponding values $Q, V, E$ and $U$ are in relation with the initially stated as

The capacitance of a metallic sphere will be $1\mu F$, if its radius is nearly