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# Electrostatic Force

## What is Electrostatic Force?

Last updated date: 28th Jan 2023
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Charge is the characteristic property of mass. There are two types of charges, positive charge and negative charge. The fundamental charge is the charge of an electron. When two charges interact with each other, then a force exists between them called electrostatic force. The magnitude of the electrostatic force between two charges is given by Coulomb's law. Here, we will discuss electrostatic force in detail and Coulomb's law which describes electrostatic force acting between two charges.

### Electrostatic Force Acting Between Two Charges

What is electrostatic force?. Electrostatic force is one of the fundamental forces in the universe.There are four fundamental forces in the universe. They are strong nuclear force, electromagnetic force , weak nuclear force and gravitational force. The electrostatic force comes under electromagnetic force. The electrostatic force exists between two charges placed at a distance. The magnitude of  electrostatic force depends on the magnitude of each charge and the distance between them.

When two positive charges or two negative charges are brought together, then the two charges repel each other. The electrostatic force acting between two like charges is called electrostatic force of repulsion. When two opposite charges are brought together, then two charges get attracted towards each other. Then the electrostatic force acting between two opposite  charges is called electrostatic force of repulsion. Therefore, we can say that like charges repel and unlike charges attract. The electrostatic force acting between two charges is greater when the magnitude of two charges are larger. The electrostatic force is larger when the distance between the two charges are less.

Let us see some electrostatic force examples .We can do a simple experiment to observe the electrostatic force. Take a piece of paper and cut it into very small pieces of paper. Then using a dry scale or ruler, rub it on your dry hair vigorously and repeat it for some time. After doing it for some time, bring the ruler close to the tiny pieces of paper. You can observe that the paper bits are attracted to the ruler. This is because when the ruler is rubbed on your dry hair, the electrons are transferred and electrostatic force acts between them which causes the paper to get attracted to the ruler. Another simple activity to visualise the electrostatic force is to move your hand closer to the screen of the tv. Then you can observe that the skin hairs are getting attracted to the screen of the TV. It is because the screen of the TV is charged due to a cathode ray tube inside the TV which polarises the skin hair and an electrostatic force will be formed that attracts the hairs of the skin. The above activities are electrostatic force examples.

### Coulomb’s Law of Electrostatic Force

The magnitude of the electrostatic force is given by Coulomb’s law. According to Coulomb's law of electrostatic force, the  electrostatic force acting between two charges is directly proportional to the product of magnitude of charges and inversely proportional to the square of the distance between the two charges.

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Consider two charges q1 and q2 placed at a distance r from each other. Then the electrostatic force acting between the two charges is given by,

${F}_{E}=\frac{k{q}_{1}{q}_{2}}{{r}^{2}}$$F_{E}=\frac{kq_{1}q_{2}}{r^{2}}$

Where,

FE - Electrostatic force between two charges q1 and q2.

k- Coulomb’s constant

q1 - magnitude of first charge

q2 - magnitude of second charge

r- Distance between two charges

The coulomb’s constant (k) is a constant which depends on the medium in which the two charges are interacting. The coulomb’s constant is given by the formula given below.

$k=\frac{1}{4\pi \epsilon }$$k=\frac{1}{4\pi \varepsilon }$

Where,

$\epsilon$$\varepsilon$ - Permittivity of the medium.

The value of  permittivity of the free space is 8.85 x 10-12 C2/Nm2 and the value of coulomb's constant of free space is 9 x 109 Nm2/C2.

Let F12 be the electrostatic force acting on the first charge due to the second charge and F21 be the force acting on the second charge due to the second charge. Then the relation between the electrostatic force acting on the two charges is given by,

F12 = - F21

The above equation means that the electrostatic force acting on two charges are equal in magnitude but opposite in direction. This is in accordance with Newton’s third law of motion. The third law of motion states that for every action, there is an equal and opposite reaction. The forces acting on two charges  F12 and F21 do not cancel each other even though they are equal in magnitude and opposite in direction. It is because they are acting on different bodies or else they would have cancelled each other.

### Solved Examples:

1. What is the electrostatic force acting between two charges having the same magnitude of $5\mu C$$5\mu C$ placed at a distance of 1 m.

Ans:

The magnitude of first charge =q1=$5\mu C$$5\mu C$

The magnitude of second charge =q2=$5\mu C$$5\mu C$

The distance between the two charges =r=1 m

The formula to calculate the electrostatic force between two charge is given by,

${F}_{E}=\frac{k{q}_{1}{q}_{2}}{{r}^{2}}$$F_{E}=\frac{kq_{1}q_{2}}{r^{2}}$

Where,

FE - Electrostatic force between two charges q1 and q2.

k- Coulomb’s constant

q1 - magnitude of first charge

q2 - magnitude of second charge

r- Distance between two charges

The value of coulomb's constant of free space is 9$×$$\times$109 Nm2/C2.

Substitute the value for the magnitude of charges and distance between the charges to obtain the electrostatic forces between two charges.

$⇒{F}_{E}=\frac{k{q}_{1}{q}_{2}}{{r}^{2}}$$\Rightarrow F_{E}=\frac{kq_{1}q_{2}}{r^{2}}$

$⇒{F}_{E}=\frac{9×{10}^{9}N{m}^{2}/{C}^{2}×5\mu C×5\mu C}{\left(1m{\right)}^{2}}$$\Rightarrow F_{E}=\frac{9\times 10^{9}Nm^{2}/C^{2}\times 5\mu C\times 5\mu C}{(1m)^{2}}$

$⇒{F}_{E}=2.25×{10}^{-1}N$$\Rightarrow F_{E}=2.25\times 10^{-1}N$

Therefore, the electrostatic force acting between the two charges is 2.25$×$$\times$10-1 N

2. The electrostatic force acting between two charges q
1 and q2  is F. What is the new electrostatic force if the distance between the two charges is doubled?

Ans:

Let r be the initial  distance between the two charges.

Then the formula to calculate initial  electrostatic force is given by,

$⇒{F}_{E}=\frac{k{q}_{1}{q}_{2}}{{r}^{2}}$$\Rightarrow F_{E}=\frac{kq_{1}q_{2}}{r^{2}}$

Where,

FE - The initial electrostatic force between two charges q1 and q2.

k- Coulomb’s constant

q1 - magnitude of first charge

q2 - magnitude of second charge

r- The initial distance between two charges

When the distance between the two charges are doubled, then new distance between the two charges r is given by,

r'=2r

The new electrostatic force F’ between the two charges when the distance gets doubled is given by,

$⇒{F}^{\prime }=\frac{k{q}_{1}{q}_{2}}{\left(2R{\right)}^{2}}$$\Rightarrow {F}'=\frac{kq_{1}q_{2}}{(2R)^{2}}$

$⇒{F}^{\prime }=\frac{k{q}_{1}{q}_{2}}{4{R}^{2}}$$\Rightarrow {F}'=\frac{kq_{1}q_{2}}{4R^{2}}$

$⇒{F}^{\prime }=\frac{{F}_{E}}{4}$$\Rightarrow {F}'=\frac{F_{E}}{4}$

Therefore, when the distance is doubled, the new electrostatic force is reduced to one fourth of the initial value.

### Conclusion

The electrostatic force can be the electrostatic force of repulsion or attraction depending on the  polarity of the two charges. The magnitude of the two charges and the distance between the two charges affects the electrostatic force. For a system of two charges, electrostatic forces on the charges are equal in magnitude but opposite in direction. The electrostatic force is a conservative force which means that the work done by the electrostatic force in a closed loop is zero. The electrostatic force also depends on the medium at which two charges are placed and is maximum when the medium is vacuum.

## FAQs on Electrostatic Force

1. Is electrostatic force a conservative force? Justify your answer.

The electrostatic force is  a conservative force. The work done by the electrostatic force does not depend on the path but depends only on the initial and the final point. Therefore, work done by the electrostatic force in a closed loop is zero because the initial and final are the same in a closed loop. Hence, the electrostatic force is a conservative force.

2. What happens when the ruler is rubbed with dry cloth and the ruler is brought near tiny pieces of paper?

When the ruler is rubbed with a dry cloth, the electrons are transferred from cloth to the ruler. Therefore, cloth becomes positive charge due to the deficiency of electrons and the ruler becomes negative charge due to extra electrons transferred from cloth to the ruler. When this ruler is brought near the tiny pieces of paper, paper bits are attracted to the ruler due to the electrostatic force.

3. Does the electrostatic force acting between two charges obey Newton's third law?

Yes, the electrostatic force acting between two charges obeys Newton’s third law. According to Newton’s third law, every action has an equal and opposite reaction. The magnitude of electrostatic acting on each charge is equal in magnitude but opposite in direction. However, these two equal and opposite electrostatic forces do not cancel each other because these forces are acting on different bodies.

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