Question

The electrostatic force on a small sphere of charge $0.4\mu C\;$due to another small sphere of charge $- 0.8\mu C\;$in air is$0.2N$.
(a) What is the distance between the two spheres?
(b) What is the force on the second sphere due to the first?

Answer 1

Hint : Electrostatic Force is one of the four fundamental forces of nature. We make use of Coulomb's Law to solve the forces created by combination of charge. First sphere has the same force as the second sphere has force.

complete step by step solution:
a) The electric force in a particle is an attractive and repulsive energy force due to electric charge. Electric energy in a body with constant charge is known as electric energy. It is known as Electrostatic force.
Electrostatic force on the first sphere of $0.4\mu C\;$due to second sphere of charge $- 0.8\mu C\;$is $F = 0.2N$
Charge on first sphere,

$${q_1} = 0.4\mu C \Rightarrow {q_1} = 0.4 \times {10^{ - 6}}C$$

Charge on second sphere,

$${q_2} = - 0.8\mu C \Rightarrow {q_2} = - 0.8 \times {10^{ - 6}}C$$

Electrostatic force between the spheres is given by the relation,
$F = \dfrac{1}{{4\pi {\varepsilon _o}}}\dfrac{{{q_1}{q_2}}}{{{r^2}}}$ (i)
And we know that $\dfrac{1}{{4\pi {\varepsilon _o}}} = 9 \times {10^9}N{m^2}{C^{ - 2}}$
Where ${\varepsilon _o} =$permittivity of free space
Now, equation (i) can be written as

$${r^2} = \dfrac{{{q_1}{q_2}}}{{4\pi {\varepsilon _o}F}} \Rightarrow {r^2} = \dfrac{{0.4 \times {{10}^{ - 6}} \times - 0.8 \times {{10}^{ - 6}}}}{{9 \times {{10}^9} \times 0.2}} \Rightarrow {r^2} = 144 \times {10^{ - 4}} \Rightarrow r = 0.12m$$

So, the distance between the two spheres is $0.12m$.

(b) Equal and Opposite Force acts on the other sphere to maintain the system in equilibrium (By Newton's Third Law).
Hence $0.2N$ force will act on the second sphere due to the first sphere.

Additional information- Coulomb's law gives the idea of ​​power between two points. By term point charge we mean that in physics the size of linearly charged bodies is much smaller than the distance between them. Therefore, we consider these to be point charges because it makes it easier for us to calculate the force of attraction / repulsion between them.
In$1784$, a French physicist, Charles-Augustine de Coulomb, measured the force between two-point charges and came up with the theory that the distances between these ball charges are inversely proportional to the square. They also found that this force was only proportional to the product of charge (amplitude only).

Note- The properties of electrostatic force are as follows:
Electrostatic energy depends on the product of the charge and inversely proportional to the square of distance between them.
For two like charge, force is repulsive in nature. While for two unlike charges, force is attractive.
Field lines for positive charge are external but field lines for negative charge are internal.
The electric field lines start from positive charge and terminate at negative charge.
Two electric field lines can never intersect.