A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by 

(1) $2\pi R^{2}E$

(2) $\pi R^2/E$

(3) $(\pi R^2-\pi R)/E$ 

(4) Zero

Electric field at a point varies as r⁰ for

(1) An electric dipole

(2) A point charge

(3) A plane infinite sheet of charge

(4) A line charge of infinite length

Total electric flux coming out of a unit positive charge put in air is 

(1) ${\epsilon }_0$

(2) ${\epsilon }_0^{-1}$

(3) ${\left(4p{\epsilon }_0\right)}^{-1}$

(4) $4\pi {\epsilon }_0$ 

A cube of side l is placed in a uniform field E, where $E=E\hat{i}$. The net electric flux through the cube is

(1) Zero

(2) l²E

(3) 4l²E

(4) 6l²E

Eight dipoles of charges of magnitude \((e)\) are placed inside a cube. The total electric flux coming out of the cube will be: 
1. \(\frac{8e}{\epsilon _{0}}\)
2. \(\frac{16e}{\epsilon _{0}}\)
3. \(\frac{e}{\epsilon _{0}}\)
4. zero

A charge q is placed at the centre of the open end of the cylindrical vessel. The flux of the electric field through the surface of the vessel is 

(1) Zero

(2) $\frac{q}{{\epsilon }_0}$

(3) $\frac{q}{2{\epsilon }_0}$

(4) $\frac{2q}{{\epsilon }_0}$ 

Electric charge is uniformly distributed along a long straight wire of radius \(1\) mm. The charge per cm length of the wire is \(Q\) coulomb. Another cylindrical surface of radius \(50\) cm and length \(1\) m symmetrically encloses the wire as shown in the figure. The total electric flux passing through the cylindrical surface is:

The S.I. unit of electric flux is 

(1) Weber

(2) Newton per coulomb

(3) Volt × metre

(4) Joule per coulomb

Shown below is a distribution of charges. The flux of electric field due to these charges through the surface S is 

(1) $3q/{\epsilon }_0$

(2) $2q/{\epsilon }_0$

(3) $q/{\epsilon }_0$ 

(4) Zero

Consider the charge configuration and spherical Gaussian surface as shown in the figure. While calculating the flux of the electric field over the spherical surface, the electric field will be due to: 

(1) q₂ only

(2) Only the positive charges

(3) All the charges

(4) +q₁ and – q₁ only