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 equal negative charges of charge – q are fixed at the points (0, a) and (0, –a) on the Y-axis. A positive charge Q is released from rest at the point (2a, 0) on the X-axis. The charge Q will:

An electrostatic line of force in the xy plane is given by equation x² + y² = 1. A particle with unit positive charge, initially at rest at the point x = 1, y = 0 in the xy plane will -

1. Not move at all

2. Will move along straight line

3. Will move along the circular line of force

4. The data given in the question is contradictory

A positively charged ball hangs from a silk thread. We put a positive test charge q₀ at a point and measure F/q₀, then it can be predicted that the electric field strength E 

(1) > F/q₀

(2) = F/q₀

(3) < F/q₀

(4) Cannot be estimated

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) $\frac{4Q}{4\pi {\epsilon }_0{R}^2}$ 

A point charge q is placed at a distance a/2 directly above the centre of a square of side a. The electric flux through the square (i.e. one face) is:

1. $\frac{q}{{\epsilon }_0}$

2. $\frac{q}{\pi {\epsilon }_0}$

3. $\frac{q}{4{\epsilon }_0}$ 

4. $\frac{q}{6{\epsilon }_0}$

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

The charge on 500 cc of water due to protons will be:

1. 6.0 × 10²⁷ C
2. 2.67 × 10⁷ C
3. 6 × 10²³ C
4. 1.67 × 10²³ C

In the given figure two tiny conducting balls of identical mass m and identical charge q hang from non-conducting threads of equal length L. Assume that θ is so small that $\tan \theta \approx \sin \theta$, then for equilibrium x is equal to 

(1) ${\left(\frac{{\displaystyle q^{2}L}}{{\displaystyle 2\pi {\epsilon }_{0}mg}}\right)}^{\frac{1}{3}}$

(2) ${\left(\frac{{\displaystyle q{L}^2}}{{\displaystyle 2\pi {\epsilon }_{0}mg}}\right)}^{\frac{1}{3}}$

(3) ${\left(\frac{{\displaystyle q^2{L}^2}}{{\displaystyle 4\pi {\epsilon }_{0}mg}}\right)}^{\frac{1}{3}}$

(4) ${\left(\frac{{\displaystyle q^{2}L}}{{\displaystyle 4\pi {\epsilon }_{0}mg}}\right)}^{\frac{1}{3}}$

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)