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

1.	execute simple harmonic motion about the origin.
2.	move to the origin and remain at rest.
3.	move to infinity.
4.	execute oscillatory but not simple harmonic motion.

An electrostatic line of force in the $xy$ plane is given by equation $x^2+y^2=1$. A particle with unit positive charge, initially at rest at the point $x=1,y=0$ in the $xy$ plane will:

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 $\frac{a}{2}$ directly above the centre of a square of side $a$. The electric flux through the square (i.e. one face) is:
1. $\frac{q}{\varepsilon_0}$
2. $\frac{q}{\pi\varepsilon_0}$
3. $\frac{q}{4\varepsilon_0}$
4. $\frac{q}{6\varepsilon_0}$

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)

Two equal charges are separated by a distance d. A third charge placed on a perpendicular bisector at x distance will experience maximum coulomb force when 

(1) $x=\frac{d}{\sqrt{2}}$

(2) $x=\frac{d}{2}$

(3) $x=\frac{d}{2\sqrt{2}}$

(4) $x=\frac{d}{2\sqrt{3}}$