Asok Kumar Das and Chittaranjan Dasgupta Solutions for Chapter: Gauss' Law and its Application, Exercise 1: EXERCISE 3

The electric field just outside the surface of a conductor has a magnitude $10 \mathrm{kN}/\mathrm{C}$ and is directed away from the conductor. What is the surface charge density of the conductor? 

If $\overrightarrow{E}=6\hat{i}+3\hat{j}+4\hat{k},$ calculate the electric flux through a surface of area $20$ units in $YZ$ -plane.

Calculate the number of electric line of force originating from a charge of $1\mathrm{C}$.

An electric flux of $-5\times {10}^3 {\mathrm{Nm}}^2{\mathrm{C}}^{-1}$ Passes through a spherical Gaussian surface of radius $20 \mathrm{cm}$ Due to the charge placed at its centre.

(i) Calculate the charge enclosed by the Gaussian surface,

An electric flux of $6\times {10}^3 {\mathrm{Nm}}^2{\mathrm{C}}^{-1}$ passes through a spherical Gaussian surface of radius $10 \mathrm{cm}$ due to the charge placed at its centre.

If the radius of the Gaussian surface is doubled how much flux would pass through the surface?

From what distance should a $100 eV$ electron by fixed towards a large metal plate having a surface charge density of $-2\times {10}^{-6}{ \mathrm{cm}}^{-2}$, so that it just fails to strike the plate ? $\left(\mathrm{e}=1.6\times {10}^{-19}\mathrm{C},{\mathrm{\epsilon }}_0=8.85\times {10}^{-12}{\mathrm{C}}^2{ \mathrm{N}}^{-1}{ \mathrm{m}}^{-2},1\mathrm{ev}=1.6\times {10}^{-19} \mathrm{J}\right)$

A sphere of metal has a radius of $12 \mathrm{cm}$ and carries a charge of $1.6\times {10}^{-7}\mathrm{C}$, distributed uniformly on its surface. Calculate the electric field intensity at a point inside the sphere.

Calculate the electric field intensity at a point, when a sphere of metal has a radius of $12 \mathrm{cm}$ And carries a charge of $1.6\times {10}^{-7}\mathrm{C}$, distributed uniformly on its surface.

(2) $18cm$ From the centre the sphere ?