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

a.	total flux through the surface of the sphere is $\frac{-\mathrm{Q}}{{\epsilon }_0}$.
b.	field on the surface of the sphere is $\frac{-Q}{4\pi {\epsilon }_0{R}^2}$.
c.	flux through the surface of the sphere due to 5Q is zero.
d.	field on the surface of the sphere due to -2Q is the same everywhere.

Choose the correct statement(s): 
1.  a and d
2.  a and c
3.  b and d
4.  c and d

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

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

If there were only one type of charge in the universe, then,

Two point dipoles of dipole moment ${\overrightarrow{\mathrm{p}}}_1$ and ${\overrightarrow{\mathrm{p}}}_2$ are at a distance x from each other and ${\overrightarrow{\mathrm{p}}}_1\left|\right|{\overrightarrow{\mathrm{p}}}_2$. The force between the dipole is:

1. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{4p_1{p}_2}{x^4}$

2. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{3p_1{p}_2}{x^3}$

3. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{6p_1{p}_2}{x^4}$

4. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{8p_1{p}_2}{x^4}$

The electric field at a point on the equatorial plane at a distance \(r\) from the centre of a dipole having dipole moment $\stackrel{}{}$\(\overrightarrow{P}\) is given by:
(\(r\gg\) separation of two charges forming the dipole, \(\epsilon_{0} =\) permittivity of free space) 
1. \(\overrightarrow{E}=\frac{\overrightarrow{P}}{4\pi \epsilon _{0}r^{3}}\) 

2. \(\overrightarrow{E}=\frac{2\overrightarrow{P}}{\pi \epsilon _{0}r^{3}}\)

3. \(\overrightarrow{E}=-\frac{\overrightarrow{P}}{4\pi \epsilon _{0}r^{2}}\)

4. \(\overrightarrow{E}=-\frac{\overrightarrow{P}}{4\pi \epsilon _{0}r^{3}}\)

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:
( \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9~ \text{Nm}^2 \text{C}^{-2}\) )

The figure shows electric field lines in which an electric dipole p is placed as shown. Which of the following statements is correct?
                      

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

A particle of mass m carrying charge -q₁ is moving around a charge +q₂ along a circular path of radius r. The period of revolution of the charge -q₁ is:

1. $\sqrt{\frac{16{\mathrm{\pi }}^3{\mathrm{\epsilon }}_0{\mathrm{mr}}^3}{{\mathrm{q}}_1{\mathrm{q}}_2}}$

2. $\sqrt{\frac{8{\mathrm{\pi }}^3{\mathrm{\epsilon }}_0{\mathrm{mr}}^3}{{\mathrm{q}}_1{\mathrm{q}}_2}}$

3. $\sqrt{\frac{{\mathrm{q}}_1{\mathrm{q}}_2}{16{\mathrm{\pi }}^3{\mathrm{\epsilon }}_0{\mathrm{mr}}^3}}$

4. zero

Point charges +4q, –q and +4q are kept on the x-axis at points x = 0, x = a and x = 2a respectively, then: