electrostatics

A uniform ring charge of radius R carries a total charge Q. Which one of the following options correctly quantifies the magnitude of the force on a point charge of strength q kept...

A uniform spherical volume charge distribution of radius 2 m, centered at the origin, has a strength of $\frac{3}{\pi} \times 10^{-6}$ C/m³. A point charge of strength $\pi \times...

In the (x, y, z) coordinate system, three point-charges Q, Q, and αQ are located in free space at (-1, 0, 0), (1, 0, 0), and (0, -1, 0), respectively. The value of α for the electr...

Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed

A thin soap bubble of radius R = 1 cm, and thickness a = 3.3 µm (a << R), is at a potential of 1 V with respect to a reference point at infinity. The bubble bursts and becomes a si...

A positive charge of 1 nC is placed at (0, 0, 0.2) where all dimensions are in metres. Consider the x - y plane to be a conducting ground plane. Take $${\varepsilon _0} = 8.85 \tim...

Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the electron and...

Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed.

In cylindrical coordinate system, the potential produced by a uniform ring charge is given $$\phi=f\left(r,\;z\right)$$, where f is a continuous function of r and z. Let $$\overrig...

A dielectric slab with 500 mm x 500 mm cross-section is 0.4 m long. The slab is subjected to a uniform electric field of $$E=6{\widehat a}_x+8{\widehat a}_y$$ kV /mm. The relative...

A capacitor is made with a polymeric dielectric having an $$\varepsilon_0$$ of 2.26 and a dielectric breakdown strength of 50 kV/cm. The permittivity of free space is 8.85 pF/m. If...

A capacitor consists of two metal plates each $$500 \times 500\,\,m{m^2}$$ and spaced $$6$$ $$mm$$ apart. The space between the metal plates is filled with a glass plate of $$4$$ $...

A parallel plate capacitor has an electrode area of $$100$$ $$m{m^2}$$, with a spacing of $$0.1$$ $$mm$$ between the electrodes. The dielectric between the plates is air with a per...

Given the potential function in free space to be $$V\left( x \right) = \left( {50{x^2} + 50{y^2} + 50{z^2}} \right)$$ volts, the magnitude (in volts /metre) and the direction of th...

The capacitance of an isolated sphere of radius 10 cm in air is equal to _____ pF.

In electrostatic field $$\nabla\times\overrightarrow E\equiv0$$

Which of the following equations represents the Gauss's law in a homogeneous isotropic medium?