Electric potential and capacitance practice · Medium

The difference between equivalent capacitances of two identical capacitors connected in parallel to that in series is $6 \mu \mathrm{F}.$ The value of capacitance of each capacitor is:

The capacitance of two concentrie spherical shells of radii $R_1$ and $R_2\left(R_2>R_1\right)$ is

An infinite sheet carrying a uniform surface charge density $\sigma$ lies on the $x y$ plane. The work done to carry a charge $q$ from the point $A=a(\hat{{i}}+2 \hat{{j}}+3 \hat{{k}})$ to the point $B=a(\hat{{i}}-2 \hat{{j}}+6 \hat{{k}})$ (where $a$ is a constant with the dimension of length and $\varepsilon_0$ is the permittivity of free space) is

A variable condenser is permanently connected to a $100\;V$ battery. If the capacity is changed from $2\mu \;F$ to $10\;\mu \;F,$ then change in energy is equal to

The potential energies associated with four orientations of an electric dipole in an electric field are:

$\text{(i)}-5 \mathrm{U}_0 \quad \text{(ii)}-7 \mathrm{U}_0 \quad$ $\text{(iii) }3 \mathrm{U}_0 \quad \text{(iv) }5 \mathrm{U}_0$

Where $\text{U}_0$ is positive. Rank the orientations according to the angle between the electric dipole moment $\overrightarrow{\mathrm{P}}$ and the electric field $\overrightarrow{\mathrm{E}}$, greatest first

Can two equipotential surfaces intersect each other?

A hollow metal sphere of radius $\text{R}$ is charged with a charge $\text{Q}.$ The electric potential and intensity inside the sphere are respectively

A uniform electric field pointing in positive x-direction exists in a region let $A$ be the origin $B$ be the point on x-axis at $x = + 1\,cm$ and $C$ be the point on y-axis at $y = + 1\,cm$. Then the potentials at points A,B, and C satisfy.

Two capacitors of capacitances $20.0 \mathrm{pF}$ and $50.0 \mathrm{pF}$ are connected in series with a $6.00 \mathrm{~V}$ battery. Find the potential difference across each capacitor.

Can a metal be used as a medium for dielectric

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 capacitor stores $10 \mu \mathrm{C}$ charge when connected across a battery. When the gap between the plates is filled with a dielectric, a charge of $20 \mu \mathrm{C}$ flows through the battery. Find the dielectric constant of the dielectric.

The potential energy of a system of two charges is negative when:

Two circular plates each of radius '$\text{r}$' and charge '$\text{q}$' form a parallel plate capacitor. Then the force of attraction between the plates is (Medium between the plate is air)

Torque acting on an electric dipole in a uniform electric field is maximum if the angle between p and E is

Stored electrostatic energy in a capacitor of capacity $C,$ which is charged upto $Q$ charge, is:

The potential energy function (in $J$) of a particle in a region of space is given as $U=\left(2 x^2+3 y^2+2 z\right)$. Hare $x, y$ and $z$ are in meter. The magnitude of $x$ component of force (in $N$) acting on the particle at point $P(1,2,3) m$ is:

A parallel plate capacitor has each plate area $A$ and separation $d$. Charge $Q$ is given to positive plate of capacitor. The force on each plate of capacitor is

Assertion: The electric potential at any point on the equatorial plane of an electric dipole is indeed zero.
Reason: The contributions to the potential from the positive and negative charges of the dipole cancel each other out due to the symmetry of the arrangement.

${Q}$ charge is given to two capacitors $C_1$ and $C_2$ which are in parallel. The charge distribution among them is

What is the angle between maximum value of potential gradient and equipotential surface?

When a test charge is brought in from infinity along the perpendicular bisector of an electric dipole, the work done is

Dielectric constant of a medium is also known as:

Assertion:- Circuits containing high capacity capacitors, charged to high voltages should be handled with caution, even when the current in the circuit is switched off.
Reason:- When an isolated capacitor is touched by hand or any other part of the human body, there is an easy path to the ground available for the discharge of the capacitor.

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

The stopping potential of anode relative to cathode that must be applied to stop the fastest photo ${e^ - }s$ emitted by surface having work function 5.01 eV, when UV light of wavelength 200 nm falls on it, must be:-

An air capacitor is connected to a battery. The effect of filling the space between the plates with a dielectric is to increase

A $500\mu F$ capacitor is charged at a steady rate of $100\mu C/\mathrm{second}.$ The potential difference across the capacitor will be $10\;V$ after an interval of

A system of two charges separated by a certain distance apart stores electrical potential energy. If the distance between them is increased, the potential energy of the system:

A hollow conducting sphere of radius $R$ has a charge $\left( { + Q} \right)$ on its surface. What is the electric potential within the sphere at a distance $r = R/3$ from its centre