Question

the electronic force on a small sphere of charge 0.4 uC due to another small sphere of charge -0.8uC in air is 0.2 N (a) what is the distance between the two sphere ? (b) what is the force on the second sphere due to the first ?

Answer 1

$\bigstar$ Question:

The electrostatic force on a small sphere of charge $\sf 0.4\: \mu C$ due to another small sphere of charge $\sf -0.8 \: \mu C$ in the air is $\sf 0.2\: C$

(a) What is the distance between the two spheres?

(b) What is the force on the second sphere due to the first?

$\bigstar$ Given:

• The charge on 1st sphere $\sf = 0.4 \times 10^{-6} C$
• The charge on 2nd sphere $\sf = -0.8 \times 10^{-6}C$
• The electrostatic force on the 1st sphere $\sf = 0.2N$

$\bigstar$ To Find:

• The distance between the two spheres.
• The force on the second sphere due to the first.

$\bigstar$ Solution:

According to the given information,

The charge on 1st sphere and 2nd sphere is $\sf 0.4 \: \mu C$ and $\sf -0.8 \times 10^{-6}C$ respectively.

Electrostatic force between the spheres is given by the relation:

$\sf F=\dfrac{1}{4\pi \epsilon_0}. \dfrac{q_1 \: q_2}{r^{2}}$

Now, here

$\sf \epsilon_0=$ Permittivity of free space

⚫ CASE I:

$\sf \dfrac{1}{4 \pi \epsilon_0} = 9 \times 10^{9}\: Nm^{2} \: C^{-2}$

$\sf r^{2} = \dfrac{1}{4 \pi \epsilon_0} . \dfrac{q_1 \: q_2}{F}$

$\sf \implies \dfrac{0.4 \times 10^{-6} \times 8 \times 10^{-6} \times 9 \times 10^{9}}{0.2}= 144 \times 10^{-4}$

$\sf r=\sqrt{144 \times 10^{-4}} =12 \times 10^{-2}= 0.12 \: m$

Therefore, the distance between the two spheres = 0.12 m

⚫ CASE II:

Since the spheres have opposite charges, the force on the second sphere due to the first sphere will also be equal to 0.2 N.

$\bigstar$ Points to Note:

➤ Electrostatics deals with the study of forces, fields and potentials arising from static charges.

➤ The three fundamental properties of the electric charge are Quantization, Additive and Conservation.

➤ Coulomb’s Law consists of constant terms which are also called a constant of proportionality and is represented by ‘k’ and it's value is $\sf 9 \times 10^{9} \: Nm^3 \: C^{-2} \: Nm^{2} C^{-2}$

➤ Superposition principle is the property of two charges to repel and attract each other remains unaffected even though there is a presence of third additional charge.