Electrostatics

An electric field of $0.01 \mathrm{~V} / \mathrm{m}$ is applied along the length of a copper wire of circular crosssection with diameter 1 mm . Copper has a conductivity of $5.8 \times 10^7 \mathrm{~S} / \mathrm{m}$. The...

In an electrostatic field, the electric displacement density vector, $$\overrightarrow D $$, is given by $$\overrightarrow D (x,y,z) = ({x^3}\overrightarrow i + {y^3}\overrightarrow j + x{y^2}\overrightarrow k )$$ C/m 2...

An electron (q 1 ) is moving in free space with velocity 10 5 m/s towards a stationary electron (q 2 ) far away. The closest distance that this moving electron gets to the stationary electron before the repulsive force d...

Concentric spherical shells of radii 2 m, 4 m, and 8 m carry uniform surface charge densities of 20 nC/m 2 , −4 nC/m 2 and ρ s ,respectively. The value of ρ s (nC/m 2 ) required to ensure that the electric flux density $...

A coaxial capacitor of inner radius 1 mm and outer radius 5 mm has a capacitance per unit length of 172 pF/m. If the ratio of outer radius to inner is doubled, the capacitance per unit length (in pF/m) is _____.

In a source free region in vacuum, if the electrostatic potential $$\varphi\;=\;2x^2\;+y^2+cz^2$$ , the value of constant c must be ________________.

If $$\overrightarrow{\mathrm E}=-\left(2\mathrm y^2\;-3\mathrm{yz}^2\right)\widehat{\mathrm x}\;-\left(6\mathrm{xy}^2-3\mathrm{xz}^2\right)\widehat{\mathrm y}+\left(6\mathrm{xyz}\right)\widehat{\mathrm z}$$ is the electr...

Medium $$1$$ has the electrical permittivity $${\varepsilon _1} = 1.5\,\,{\varepsilon _0}\,\,\,F/m$$ and occupies the region to left of $$x = 0$$ plane. Medium $$2$$ has the electrical permittivity $${\varepsilon _2} = 2...

If the electric field intensity is given by $$\mathrm E=\left(\mathrm x{\widehat{\mathrm u}}_\mathrm x\;+\mathrm y{\widehat{\mathrm u}}_\mathrm y+\mathrm z{\widehat{\mathrm u}}_\mathrm z\right)\;\mathrm{volt}/\mathrm m$$...

An electric field on a plane is described by its potential V = $$20\left(r^{-1}\;+\;r^{-2}\right)$$ where r is the distance from the source. The field is due to

A metal sphere with 1 m radius and a surface charge density of 10 Coulombs/m 2 is enclosed in a cube of 10 m side. The total outward electric displacement normal to the surface of the cube is

The electric field strength at a distance point, P, due to a point charge, +q, located at the origin, is 100 $$\mu $$V/m. If the point charge is now enclosed by a perfectly conducting metal sheet sphere whose center is a...

In the infinite plane, y = 6 m, there exists a uniform surface charge density of (1/6000$$\pi $$) $$\mu $$C/m 2 . The associated electric field strength is:

The electric field strength at a far-off point P due to a point charge + q, located at the origin O is 100 millivolts/metre. The point charge is now enclosed by a perfectly conducting hollow metal sphere with its centre...

On either side of a charge-free interface between two media,