Two-point charges \(+8q\)  and \(-2q\) are located at \(x=0\)  and \( x = L\) respectively. The location of a point on the \(x-axis\)  at which the net electric field due to these two point charges is zero is 

1.	\(8~\text{L}\)	2.	\(4~\text{L}\)
3.	\(2~\text{L}\)	4.	\(\frac{\text{L}}{4}\)

Three infinitely long charge sheets are placed as shown in the figure. The electric field at point P is 

(1) $\frac{2\sigma }{{\epsilon }_o}\hat{k}$

(2) $-\frac{2\sigma }{{\epsilon }_o}\hat{k}$

(3) $\frac{4\sigma }{{\epsilon }_o}\hat{k}$

(4) $-\frac{4\sigma }{{\epsilon }_o}\hat{k}$

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

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) $\frac{2q}{{\epsilon }_0}$ 

\(q_1, q_2,q_3~\text{and}~q_4\) are point charges located at points as shown in the figure and \(S\) is a spherical Gaussian surface of radius \(R\). Which of the following is true according to the Gauss’s law?

1. \(\oint_s\left(\vec{E}_1+\vec{E}_2+\vec{E}_3\right) \cdot d \vec{A}=\frac{q_1+q_2+q_3}{2 \varepsilon_0}\)
2. \(\oint_s\left(\vec{E}_1+\vec{E}_2+\vec{E}_3+\vec{E}_4\right) \cdot d \vec{A}=\frac{\left(q_1+q_2+q_3\right)}{\varepsilon_0}\)
3. \(\oint_s\left(\vec{E}_1+\vec{E}_2+\vec{E}_3\right) \cdot d \vec{A}=\frac{\left(q_1+q_2+q_3+q_4\right)}{\varepsilon_0}\)
4. \(\oint_s\left(\vec{E}_1+\vec{E}_2+\vec{E}_3+\vec{E}_4\right) \cdot d \vec{A}=\frac{\left(q_1+q_2+q_3+q_4\right)}{\varepsilon_0}\)

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

The electric intensity due to an infinite cylinder of radius R and having charge q per unit length at a distance r(r > R) from its axis is 

(1) Directly proportional to r²

(2) Directly proportional to r³

(3) Inversely proportional to r

(4) Inversely proportional to r²

Two infinitely long parallel wires having linear charge densities λ₁ and λ₂ respectively are placed at a distance of R meters. The force per unit length on either wire will be $\left(K=\frac{{\displaystyle 1}}{{\displaystyle 4\pi {\epsilon }_0}}\right)$

(1) $K\frac{2{\lambda }_1{\lambda }_2}{R^2}$

(2) $K\frac{2{\lambda }_1{\lambda }_2}{R}$

(3) $K\frac{{\lambda }_1{\lambda }_2}{R^2}$ 

(4) $K\frac{{\lambda }_1{\lambda }_2}{R}$