In finding the electric field using Gauss Law the formula $|\overrightarrow{\mathrm{E}}|=\frac{q_{\mathrm{enc}}}{\varepsilon_{0}|\mathrm{A}|}$ is applicable. In the formula $\varepsilon_{0}$ is permittivity of free space, $A$ is the area of Gaussian surface and $q_{enc}$ is charge enclosed by the Gaussian surface. The equation can be used in which of the following situation?
Only when the Gaussian surface is an equipotential surface
Only when $|\overrightarrow{\mathrm{E}}|=$ constant on the surface.
For any choice of Gaussian surface.
Only when the Gaussian surface is an equipotential surface and $|\overrightarrow{\mathrm{E}}|$ is constant on the surface.
A cubical volume is bounded by the surfaces $x =0, x = a , y =0, y = a , z =0, z = a$. The electric field in the region is given by $\overrightarrow{ E }= E _0 \times \hat{ i }$. Where $E _0=4 \times 10^4 NC ^{-1} m ^{-1}$. If $a =2 cm$, the charge contained in the cubical volume is $Q \times 10^{-14} C$. The value of $Q$ is $...........$
Take $\left.\varepsilon_0=9 \times 10^{-12} C ^2 / Nm ^2\right)$
A charge $q$ is placed at the centre of the open end of cylindrical vessel. The flux of the electric field through the surface of the vessel is
The electric field components in Figure are $E_{x}=\alpha x^{1 / 2}, E_{y}=E_{z}=0,$ in which $\alpha=800 \;N / C\, m ^{1 / 2} .$ Calculate
$(a)$ the flux through the cube, and
$(b)$ the charge within the cube. Assume that $a=0.1 \;m$
An electric field is uniform, and in the positive $x$ direction for positive $x,$ and uniform with the same magnitude but in the negative $x$ direction for negative $x$. It is given that $E =200 \hat{ i }\; N/C$ for $x\,>\,0$ and $E = - 200\hat i\;N/C$ for $x < 0 .$ A right ctrcular cyllnder of length $20 \;cm$ and radius $5\; cm$ has its centre at the origin and its axis along the $x$ -axis so that one face is at $x=+10\; cm$ and the other is at $x=-10\; cm$
$(a)$ What is the net outward flux through each flat face?
$(b)$ What is the flux through the side of the cylinder?
$(c)$ What is the net outward flux through the cylinder?
$(d)$ What is the net charge inside the cyllnder?
A hollow cylinder has a charge $q$ coulomb within it. If $\phi$ is the electric flux in units of $volt-meter$ associated with the curved surface $B,$ the flux linked with the plane surface $A$ in units of $V-m$ will be