What is the potential energy of two equal positive point charges of \(1~ \mu \text{C}\) each held \(1\) m apart in the air?

1.	\(9 \times 10^{-3}~\text{J}\)	2.	\(9 \times 10^{-3}~\text{eV}\)
3.	\(2~\text{eV/m}\)	4.	zero

Ten electrons are equally spaced and fixed around a circle of radius R. Relative to V = 0 at infinity, the electrostatic potential V and the electric field E at the centre C are:

A cube of a metal is given a positive charge Q. For the above system, which of the following statements is true?

Three charges \(Q\), \(+q \) and \(+q \) are placed at the vertices of an equilateral triangle of side \(l\) as shown in the figure. If the net electrostatic energy of the system is zero, then \(Q\) is equal to:

A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the shell. The electrostatic potential at a point p which is at a distance $\frac{R}{2}$ from the centre of the shell is:

1. $\frac{(q+Q)}{4\pi {\epsilon }_0}\frac{2}{R}$

2. $\frac{2Q}{4\pi {\epsilon }_{0}R}$

3. $\frac{2Q}{4\pi {\epsilon }_{0}R}-\frac{2q}{4\pi {\epsilon }_{0}R}$

4. $\frac{2Q}{4\pi {\epsilon }_{0}R}+\frac{q}{4\pi {\epsilon }_{0}R}$

A charge of 10 e.s.u. is placed at a distance of 2 cm from a charge of 40 e.s.u. and 4 cm from another charge of 20 e.s.u. The potential energy of the charge 10 e.s.u. is: (in ergs) 

In a certain charge distribution, all points having zero potential can be joined by a circle S. Points inside S have positive potential, and points outside S have a negative potential. A positive charge, which is free to move, is placed inside S. What is the correct statement about S:

Two charges q₁ and q₂ are placed 30 cm apart, as shown in the figure. A third charge q₃ is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is $\frac{q_3}{4\pi {\epsilon }_0}k$, where k is:

If the dielectric constant and dielectric strength be denoted by k and x respectively, then a material suitable for use as a dielectric in a capacitor must have:

1. high k and high x.

2. high k and low x.

3. low k and low x.

4. low k and high x.

Three capacitors of capacitances 3 μF, 9 μF and 18 μF are connected once in series and another time in parallel. The ratio of equivalent capacitance in the two cases $\left(\frac{{\displaystyle C_s}}{{\displaystyle C_p}}\right)$ will be:

1. 1 : 15

2. 15 : 1

3. 1 : 1

4. 1 : 3