The $S.I.$ unit of electric flux is
Weber
Newton per coulomb
Volt $×$ metre
Joule per coulomb
An infinitely long thin non-conducting wire is parallel to the $z$-axis and carries a uniform line charge density $\lambda$. It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $PQ$ subtends an angle $120^{\circ}$ at the centre $O$ of the spherical shell, as shown in the figure. The permittivity of free space is $\epsilon_0$. Which of the following statements is (are) true?
$(A)$ The electric flux through the shell is $\sqrt{3} R \lambda / \epsilon_0$
$(B)$ The z-component of the electric field is zero at all the points on the surface of the shell
$(C)$ The electric flux through the shell is $\sqrt{2} R \lambda / \epsilon_0$
$(D)$ The electric field is normal to the surface of the shell at all points
The figure shows the electric field lines of three charges with charge $+1, +1$, and $-1$. The Gaussian surface in the figure is a sphere containing two of the charges. The total electric flux through the spherical Gaussian surface is
Given below are two statements:
Statement $I :$ An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.
Statement $II :$ If $R$ is the radius of a solid metallic sphere and $Q$ be the total charge on it. The electric field at any point on the spherical surface of radius $r ( < R )$ is zero but the electric flux passing through this closed spherical surface of radius $r$ is not zero.
In the light of the above statements, choose the correct answer from the options given below:
Linear charge density of wire is $8.85\,\mu C/m$ . Radius and height of the cylinder are $3\,m$ and $4\,m$ . Then find the flux passing through the cylinder
Explain electric flux.