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

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

An electric charge q is placed at the centre of a cube of side a. The electric flux on one of its faces will be:
(1) $\frac{q}{6{\epsilon }_0}$
(2) $\frac{q}{{\epsilon }_0{a}^2}$
(3) $\frac{q}{4\pi {\epsilon }_0{a}^2}$
(4) $\frac{q}{{\epsilon }_0}$ 

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

According to Gauss’ Theorem, electric field of an infinitely long straight wire is proportional to 
(1) r
(2) $\frac{1}{r^2}$
(3) $\frac{1}{r^3}$
(4) $\frac{1}{r}$

\(q_1, q_2,q_3~\text{and}~q_4\) 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. \(\oint_s\left(\vec{E}_1+\vec{E}_2+\vec{E}_3+\vec{E}_4\right) \cdot d \vec{A}=\frac{\left(q_1+q_2+q_3+q_4\right)}{\varepsilon_0}\)

If the electric flux entering and leaving an enclosed surface respectively is ${\phi }_1$ and ${\phi }_2$, the electric charge inside the surface will be: 
(1) $({\phi }_1+{\phi }_2){\epsilon }_0$
(2) $({\phi }_2-{\phi }_1){\epsilon }_0$
(3) $({\phi }_1+{\phi }_2)/{\epsilon }_0$
(4) $({\phi }_2-{\phi }_1)/{\epsilon }_0$ 

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

A solid metallic sphere has a charge +3Q. Concentric with this sphere is a conducting spherical shell having charge –Q. The radius of the sphere is a and that of the spherical shell is b (b > a). What is the electric field at a distance R(a < R < b) from the centre 
(1) $\frac{Q}{2\pi {\epsilon }_{0}R}$
(2) $\frac{3Q}{2\pi {\epsilon }_{0}R}$
(3) $\frac{3Q}{4\pi {\epsilon }_0{R}^2}$
(4) $\frac{4Q}{4\pi {\epsilon }_0{R}^2}$ 

Three positive charges of equal value q are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in 
(1)   (2)
(3)    (4)

Three charges –q₁, +q₂ and –q₃ are placed as shown in the figure. The x-component of the force on –q₁ is proportional to 

(1) $\frac{q_2}{b^2}-\frac{q_3}{a^2}\sin \theta$
(2) $\frac{q_2}{b^2}-\frac{q_3}{a^2}\cos \theta$
(3) $\frac{q_2}{b^2}+\frac{q_3}{a^2}\sin \theta$
(4) $\frac{q_2}{b^2}+\frac{q_3}{a^2}\cos \theta$

Which of the following graphs shows the variation of electric field E due to a hollow spherical conductor of radius R as a function of distance from the centre of the sphere 

1.		2.
3.		4.

(1)
(2)
(3)
(4)

Two concentric conducting thin spherical shells \(A\) and \(B\) having radii \(r_A\) and \(r_B\) \((r_B>r_A)\) are charged to \(Q_A\) and $$\(-Q_B~(|Q_B|>|Q_A|).\) The electrical field at distance \(x\) from the common center is:

1.		2.
3.		4.

Two identical charged spheres suspended from a common point by two massless strings of lengths l are initially at a distance d(d < < l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then, v varies as a function of the distance x between the sphere, as:
1. \(v \propto x\)
2. \(v \propto x^{\frac{-1}{2}}\)
3. \(v \propto x^{-1}\)
4. \(v \propto x^{\frac{1}{2}}\)${\frac{\mathrm{}}{}}^{}$
 

Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become:

1. (1/√2)²
2. $(r/\sqrt[3]{2})$
3. (2r/√3)
4. (2r/3)

What is the flux through a cube of side 'a' if a point charge q is at one of its corners?
1. $\frac{2q}{{\epsilon }_0}$                                         
2. $\frac{q}{8{\epsilon }_0}$
3. $\frac{q}{{\epsilon }_0}$                                         
4. $\frac{q}{2{\epsilon }_0}6a^2$

A surface of side L metre in the plane of the paper is placed in a uniform electric field E(volt/m) acting along the same plane at an angle $\theta$ with the horizontal side of the square as shown in figure. The electric flux linked to the surface in unit of V-m, is

(1) EL² 
(2) EL²cos$\theta$
(3) EL²sin$\theta$
(4) 0

The electric field at a distance $\frac{3\mathrm{R}}{2}$ from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance $\frac{\mathrm{R}}{2}$ from the centre of the sphere is 
1. $\mathrm{zero}$                                     2. $E$
3. $\frac{E}{2}$                                       4. $\frac{E}{3}$