q \(\rightarrow\)_______Q
1/2 mv2 = kQq/r
Or, v2 a1/r
Or, r a 1/v²
Or, r' = r/4

The principle of superposition states that total force on a given charge is the vector sum of the individual forces exerted on it by all other charges, the force between two charges being exerted in such a manner as if all other charges were absent
\(\overrightarrow { F } =\overrightarrow { F_{ 12 } } +\overrightarrow { F_{ 13 } } +....+\overrightarrow { F_{ 1N } } \)

q₁ = +\(\mu C\), q₂ = +6\(\mu C\), F = 12N
\(q_{1}^{'}=+2-4=-2\mu C;\) \(q_2^{'}=+6-4=2\mu C\) 
F' = ?
\({F'\over F}={(q_1^{'})(q_2^{'})\over q_1q_2}={(-2)(2)\over(2)(6)}=-{1\over 3}\)
\(F'={-F\over 3}={-12\over 3}=-4 N\)(attractive)

In a satellite, there is a condition of weightlessness. Therefore, mg = 0. On account of electrostatic force of repulsion between the balls, the strings would become horizontal. Therefore, angle between the strings = 180^o.
Also, tension in each string = force of repulsion 
\(T={1\over 4\pi\epsilon_o}{q^2\over(2l)^2}N\)

Given,
The area of plate of the capacitor, A = 6 x 10^-3 m²
Distances between the plates, d = 3mm = 3 x 10^-3 m
Voltage supplied, V = 100V
Capacitance of a parallel plate capacitor is given by, \(C=\frac{\epsilon \times A}{d}\) 
Here,
ε = permittivity of free space = 8.854 x10^-12 N^-1 m ^-2 C^-2
\(C=\frac{8.854 \times 10^{-12} \times 6 \times 10^{-3}}{3 \times 10^{-3}}=17.81 \times 10^{-12} \mathrm{~F}=17.71 \mathrm{pF}\)
Therefore, each plate of the capacitor is having a charge of
q = VC = 100 x 17.81 x 10^-12 C = 1.771 x 10^-9 C

\(3\mu F\)

When a charged rod is brought near a piece of paper, equal and opposite charge is induced on the paper. The force of attraction between the glass rod and the piece of paper is more than the force of repulsion between the glass rod and piece of paper. Hence the charged glass rod attract the piece of paper.

(a) We know that the net field inside a charged conductor is zero i.e. 
\(\overrightarrow { E } \) = 0, inside
Let us choose a gaussian surface lying wholly within the conductor and enclosing the cavity.
According to Gauss' law,
\(\oint \overrightarrow { E } .\overrightarrow { dS } =\frac { q }{ { \varepsilon }_{ 0 } } =0\)  \((\because \overrightarrow { E } =0,inside)\)
\(\therefore \) q = 0 i.e. charge inside the cavity is zero. Hence the entire charge Q on the conductor must appear on the outer surface of the conductor.
(b) The conductor B carrying a charge + q inseted in the cavity induces a charge - q on the metal surface of cavity and + q on the outside surface of the conductor A [Fig (b)]. As the outer surface of A originally had a charge Q, the total charge on it would become (Q + q).
(c) To shift a sensitive instrument from the strong electrostatic fields in its environment, enclose the instrument fully by a metallic surface.

Given q₁ = 2 \(\times\) 10^-7 C, q₂ = 3 \(\times\) 10^-7 C   r = 30 cm = 0.3 m
Therefore, Force of repulsion, F = 9 \(\times\) 10⁹ \(\times\) \(\frac { { q }_{ 1 }{ q }_{ 2 } }{ { r }^{ 2 } } \)
= \(9\times { 10 }^{ 9 }\times \frac { 2\times { 1 }0^{ -7 }\times 3\times { 10 }^{ -7 } }{ { (0.3) }^{ 2 } } =\frac { 54\times { 10 }^{ -5 } }{ 9\times { 10 }^{ -2 } } \)
 \(=\ 6\times { 10 }^{ -3 }N\)

(a) Helping, sharing, respect for elderly people.
(b) For a body to get positively charged, a negatively charged body has to brought close to the neutral body which after earthing gets charged uniformly.

Yes, it is true. Every conductor/insulator is electrically neutral, as it contains equal amounts of positive charge and negative charge.
This statement is true. Charging lies in charge imbalance. When a body loses some electrons, it becomes positively charged because it has excess of protons over electrons. The reverse is also true.
Nature/God has created the universe. In original, all bodies are neutral with no forces of attraction/repulsion. When interests of any two persons clash (i.e. two bodies are rubbed against each other), they become charged. From the charging, the forces of attraction/repulsion arises, i.e. pulls and pressures of life.
Nature/God wants us to live in peace without stress and tensions in life. We get charged over petty things in life and invite all sorts of pulls, pressures and tensions.

(i) Examples of paramagnetic material are aluminum; chromium; oxygen.
(ii) Iron and cobalt are two ferromagnetic materials. The ferromagnetic substances, but to a much larger degree. For example, relative magnetic permeability of paramagnetic substances is slightly greater than 1

Charge on the \(4\mu F\) capacitor when it is charged to 200 V.
\(Q=CV=(4\times { 10 }^{ -6 }F)(200\quad V)=8\times { 10 }^{ -4 }C\)
This charged capacitor is then connected to an unchanged capacitor of capacitance \(2\mu F\)
So \({ C }^{ ' }=(4+2)\mu F=6\mu F\)
The charge capacitor is then capacitor is now shared between the two until they attain a common potential.
The  common potential after the combination
\(=\frac { Q }{ { C }^{ ' } } =\frac { 8\times { 10 }^{ -4 }C }{ 6\times { 10 }^{ -6 }F } =1.33\times { 10 }^{ 2 }V=133V\)
The electrical potential energy of the first capacitor before it is connected to the second
\(=\frac { 1 }{ 2 } { CV }^{ 2 }=\frac { 1 }{ 2 } (4\times { 10 }^{ -6 }){ (200) }^{ 2 }\)
\(=8\times { 10 }^{ -2 }J\)
The electrical potential energy of the system after they are connected
\(=\frac { 1 }{ 2 } { { C }^{ ' }{ V }^{ ' } }^{ 2 }=\frac { 1 }{ 2 } \left( 6\times { 10 }^{ -6 } \right) { (200) }^{ 2 }=5.30\times { 10 }^{ -2 }J\)
Energy in the form of heat and electromagnetic radiation
\(=\left( 8\times { 10 }^{ -2 }-5.3\times { 10 }^{ -2 } \right) J=2.7\times { 10 }^{ -2 }J\)