Consider a region inside where there are various types of charges but the total charge is zero. At points outside the region:

(a)	the electric field is necessarily zero.
(b)	the electric field is due to the dipole moment of the charge distribution only.
(c)	the dominant electric field is \(\propto \dfrac 1 {r^3}\), for large \(r\), where \(r\) is the distance from the origin in this region.
(d)	the work done to move a charged particle along a closed path, away from the region, will be zero.

Which of the above statements are true?
1. (b) and (d)
2. (a) and (c)
3. (b) and (c)
4. (c) and (d)

Refer to the arrangement of charges in the figure and a Gaussian surface of a radius \(R\) with \(Q\) at the centre. Then:

Choose the correct statement(s): 

The acceleration of an electron due to the mutual attraction between the electron and a proton when they are \(1.6~\mathring{A}\) apart is:
\(\left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9~ \text{Nm}^2 \text{C}^{-2}\right)\)

In the figure given below, two positive charges \(q_2\) and \(q_3\) fixed along the \(y\)-axis, exert a net electric force in the \(+x\text-\)direction on a charge \(q_1\) fixed along the \(x\)-axis. If a positive charge \(Q\) is added at \((x, 0),\) the force on \(q_1\):

A point positive charge is brought near an isolated conducting sphere (figure). The electric field is best given by:

1.		2.
3.		4.

The electric flux through the surface:

Five charges \(q_1, q_2, q_3, q_4~\text{and}~q_5\) are fixed at their positions as shown in the figure, \(S\) is a Gaussian surface. The Gauss' law is given by \(\int_{S}E\cdot dS= \frac{q}{\varepsilon_0}\). Which of the following statements is correct?