Electrostatic Potential and Capacitance

The value of electric potential at a distance of 9 cm from the point charge \(4\times {10}^{-7}\mathrm{C}\) is [Given \(\left.\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}{\mathrm{Nm}}^{2}{\mathrm{C}}^{-2}\right]\) :

Which of the following statements are correct?
A. Inside a conductor, the electrostatic field is zero.
B. Electric field at the surface of a charged conductor does not depend on its surface charge density.
C. The interior of a charged conductor can have no excess charge in the static situation.
D. At the surface of a charged conductor, the electrostatic field must be normal to the surface at every point.
E. The electrostatic potential is zero everywhere inside a charged conductor.
Choose the correct answer from the options given below:

The capacitance of a capacitor with charge \(\mathrm{q}\) and a potential difference \(V\) depends on :[Re-NEET 2024]

The capacitance of a capacitor with charge \(\mathrm{q}\) and a potential difference \(V\) depends on :

The value of electric potential at a distance of 9 cm from the point charge \(4\times {10}^{-7}\mathrm{C}\) is [Given \(\left.\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}{\mathrm{Nm}}^{2}{\mathrm{C}}^{-2}\right]\) :

If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then

A. the charge stored in it, increases.

B. the energy stored in it, decreases.

C. its capacitance increases.

D. the ratio of charge to its potential remains the same.

E. the product of charge and voltage increases.

Choose the most appropriate answer from the options given below:

[NEET 2024]

Consider two uncharged capacitors of equal capacitance 200 pF. One of them is charged by a 100 V supply and disconnected. Now this capacitor is connected to the uncharged capacitor. The amount of electrostatic energy lost in the process is:

The value of electric potential at a distance of 9 cm from the point charge \(4\times {10}^{-7}\mathrm{C}\) is [Given \(\left.\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}{\mathrm{Nm}}^{2}{\mathrm{C}}^{-2}\right]\) :

A \(12\mathrm{pF}\) capacitor is connected to a \(50\mathrm{V}\) battery, the electrostatic energy stored in the capacitor in \(\mathrm{nJ}\) is

[Re-NEET 2024]

The capacitance of a parallel plate capacitor with air as medium is \(3\mu F\). With the introduction of a dielectric medium between the plates, the capacitance becomes \(15\mu F\). The permittivity of the medium is

[NEET 2020]

Two capacitors of capacities \(2 C\) and \(C\) are joined in parallel and charge up to potential \(V\). The battery is removed and the capacitor of capacity \(C\) is filled completely with a medium of dielectric constant \(K\). The potential difference across the capacitors will now be:

[JEE Main 2021, 27 Jul (Shift 1)]

Two charged spherical conductors of radius R₁ and R₂ are connected by a wire. Then the ratio of surface charge densities of the spheres \(\left(\frac{{\sigma }_{1}}{{\sigma }_{2}}\right)\) is:

[NEET 2021]

Twenty seven drops of same size are charged at \( 220 \mathrm{~V} \) each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

[NEET 2021]

The angle between the electric lines of force and the equipotential surface is :

The distance between two plates of a capacitor is \(d\) and its capacitance is \(C_1\), when air is the medium between the plates. If a metal sheet of thickness \(\frac{2 d}{3}\) and of same area as plate is introduced between the plates, the capacitance of the capacitor becomes \(C_2\). The ratio \(\frac{C_2}{C_1}\) is:

The electric potential \(V\) is given as a function of distance \(\times\) (metre) by \(V=\left(5 x^2+10 x-4\right)\) volt. Value of electric field at \(x=1 \mathrm{~m}\) is

A parallel plate capacitor with plate area ' \(A\) ' and distance of separation ' \(d\) ' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as:
\[\begin{aligned}& \varepsilon(x)=\varepsilon_0+k x, \text { for }\left(0

Two identical electric point dipoles have dipole moments \(\overrightarrow{p_1}=p \hat{i}\) and \(\overrightarrow{p_2}=-p \hat{i}\) are held on the \(x\) axis at distance ' \(a\) ' from each other. When released, they move along the \(x\)-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is ' \(m\) ', their speed when they are infinitely far apart is:

[JEE Main 2020, 6 Sep (Shift 2)]

Polar molecules are the molecules:

Two capacitors of capacities \(2 C\) and \(C\) are joined in parallel and charge up to potential \(V\). The battery is removed and the capacitor of capacity \(C\) is filled completely with a medium of dielectric constant \(K\). The potential difference across the capacitors will now be:

In a certain region of space with volume \( 0.2 \mathrm{~m}^{3} \), the electric potential is found to be \( 5 \mathrm{~V} \) throughout. The magnitude of electric field in this region is:

[NEET 2020]

Two isolated metallic solid spheres of radii \(R\) and \(2 R\) are charged such that both have same charge density \(\sigma\). The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is \(\sigma^{\prime}\). The ratio \(\frac{\sigma^{\prime}}{\sigma}\) is: