Electrical Force - Definition, Diagram, Examples, Coulomb's Law, FAQs

What is Electric Force?

Electric force is the force of attraction or repulsion that exists between electrically charged particles. It is one of the fundamental forces of nature and plays an important role in the study of electrostatics.

When two charged bodies are brought near each other, they exert forces on one another. Like charges repel each other, whereas unlike charges attract each other. This force acts along the line joining the centres of the two charges.

The magnitude of electric force depends on the amount of charge on the bodies and the distance between them. It is governed by Coulomb’s law and acts even without physical contact between the charges.

Thus, electric force is defined as the force experienced by a charged particle in the presence of another charge.

• Like charges (both positive or both negative) repel each other.
• Unlike Charges (one positive and one negative) attracts each other.

Simply we can say that Electric force is the force exerted between two electrically charged objects. This force is a vector quantity, meaning it has both magnitude and direction. The direction of the electric force depends on whether the charges are alike (repulsive force) or different (attractive force).

What is the S.I. Unit of Electric Force?

The SI unit of electric force is the Newton (N).

What is Coulomb’s law?

The electric force is described by Coulomb's Law, which states that the magnitude of the force $F$ between two point charges $q_1$ and $q_2$ separated by a distance $r$ is given by:

$
F=k_e \frac{\left|q_1 q_2\right|}{r^2}
$

where:

• $k_e$ is Coulomb's constant $\left(8.99 \times 10^9 \mathrm{~N} \mathrm{~m}^2 / \mathrm{C}^2\right)$,
• $\left|q_1 q_2\right|$ is the product of the magnitudes of the two charges,
• $r$ is the distance between the charges.

Also read -

• NCERT Exemplar Solutions for All Subjects
• NCERT Solutions for All Subjects
• NCERT Notes For All Subjects

Electric Constant (Permittivity of Free Space)

The electric constant, denoted by $\epsilon_0$, is also known as the permittivity of free space. It is a fundamental physical constant that describes how an electric field behaves in a vacuum.

It represents the ability of free space to permit electric field lines. In other words, it determines the strength of the electric force between two charges placed in vacuum.

The value of permittivity of free space is:

$
\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}
$

It appears in Coulomb's law in the form:

$
F=\frac{1}{4 \pi \epsilon_0} \cdot \frac{q_1 q_2}{r^2}
$

Thus, $\epsilon_0$ plays a crucial role in determining the magnitude of electrostatic forces and electric fields in vacuum.

Limitations of Coulomb’s Law

Coulomb’s law gives the force between two point charges under ideal conditions. However, it has certain limitations.

• It is applicable only to point charges, i.e., when the size of the charged bodies is negligible compared to the distance between them. For extended bodies, the distribution of charge must be considered.
• The law is valid only for charges at rest. When charges are in motion, magnetic effects arise, and Coulomb’s law alone is not sufficient to describe the interaction.
• It assumes that the medium between the charges is homogeneous and isotropic. In non-uniform media, the relation may not hold accurately.
• At very small distances, such as atomic or subatomic scales, Coulomb’s law fails due to quantum mechanical effects.

Electric Force Examples

The following are the electric force examples

1. Static Hair Attraction: When a balloon is rubbed on hair head, then it will catch hair strands because of the formation of opposite charges.
2. Lightning: When there is a difference between oppositely charged ground and cloud then there will be lightning.
3. Charged Comb and Paper: Small paper pieces attracts to a comb when its is charged.
4. Dust Attraction: Dust sticks to TV or computer screens due to electric charges present on their surfaces.
5. Clothes Sticking Together: Clothes stick together from static electricity after drying.

What is Electrostatic Force?

Force that occurs between two charged objects that are at rest (stationary), is called as Electrostatic Force. Electrostatic Force follows Coulomb's law.

Examples of Electrostatic Force In Our Daily Life

There are a lot of examples of electrostatic force in our daily life. Some of them are mentioned below.

• Nylon Rubbing
• Charged Comb
• Doorknob
• Woollen Clothes
• Television screen
• Photocopier

Uses of Electric Force

• Electric force is used in electrostatic precipitators to remove dust and smoke particles from industrial gases.
• It is used in photocopiers and laser printers to transfer charged ink onto paper.
• Electric force is applied in electrostatic spray painting to obtain a uniform coating with less wastage of paint.
• It explains natural phenomena like lightning, which occurs due to attraction between charged clouds and the earth.
• Electric force plays an important role in the structure of atoms, holding electrons and protons together.
• It is used in various electronic devices, especially in components like capacitors for storing electrical energy.

Solved Example on Electric Force

Q1. Find the Electric Force between two protons.

Solution.

$
F_e=\frac{k_e \cdot e^2}{r^2}
$

where:
$k_e=9 \times 10^9 \mathrm{~N} \mathrm{~m}^2 / \mathrm{C}^2$
$e=1.6 \times 10^{-19} \mathrm{C}$
$r=1 \times 10^{-15} \mathrm{~m}$

1. Square the charge $e$ :

$
e^2=\left(1.6 \times 10^{-19}\right)^2=2.56 \times 10^{-38} \mathrm{C}^2
$

2. Square the distance $r$ :

$
r^2=\left(1 \times 10^{-15}\right)^2=1 \times 10^{-30} \mathrm{~m}^2
$

3. Substitute these values into Coulomb's Law:

$
F_e=\frac{9 \times 10^9 \times 2.56 \times 10^{-38}}{1 \times 10^{-30}}
$

4. Simplify the calculation:

$
F_e=9 \times 10^9 \times 2.56 \times 10^{-8}
$

5. Final calculation:

$
F_e=230.4 \mathrm{~N}$

Q2. What is the magnitude of the force that a 25μC charge exerts on a −10μC charge placed at a distance of 8.5cm ?

Solution:

$
F=k_e \frac{q_1 \cdot q_2}{r^2}
$

where:
$k_e=9 \times 10^9 \mathrm{~N} \mathrm{~m}^2 / \mathrm{C}^2$
$q_1=+25 \mu \mathrm{C}=+25 \times 10^{-6} \mathrm{C}$
$q_2=-10 \mu \mathrm{C}=-10 \times 10^{-6} \mathrm{C}$
$r=8.5 \mathrm{~cm}=0.085 \mathrm{~m}$

1. Substitute the values:

$
F=9 \times 10^9 \cdot \frac{\left(25 \times 10^{-6}\right) \cdot\left(-10 \times 10^{-6}\right)}{(0.085)^2}
$

2. Calculate the product of charges:

$
q_1 \cdot q_2=25 \times 10^{-6} \cdot\left(-10 \times 10^{-6}\right)=-2.5 \times 10^{-10} \mathrm{C}^2
$

3. Square the distance:

$
r^2=(0.085)^2=0.007225 \mathrm{~m}^2
$

4. Substitute these values back:

$
F=9 \times 10^9 \cdot \frac{-2.5 \times 10^{-10}}{0.007225}
$

5. Calculate the division:

$
F=9 \times 10^9 \cdot\left(-3.46 \times 10^{-8}\right)
$

6. Final multiplication:

$
F=-311.42 \mathrm{~N}
$

NOTE: The negative sign in the electric force indicates that the forces between the given two-particle are attractive in nature.