What is the concept development practice page 32-1 coulomb’s law?

concept development practice page 32-1 Coulomb’s law

Coulomb’s Law is a fundamental principle in physics that describes the force between two electrically charged objects. Named after the French physicist Charles-Augustin de Coulomb, this law is crucial in understanding electrostatic interactions, which play a vital role in various fields, from physics and chemistry to engineering and technology.

What is Coulomb’s Law?

Coulomb’s Law states that the electrostatic force $F$ between two point charges q1q_1q1​ and q2q_2q2​ is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance $r$ between them. Mathematically, it is expressed as:

F=k∣q1q2∣r2F = k \frac{|q_1 q_2|}{r^2}F=kr2∣q1​q2​∣​

Where:

• $F$ = Electrostatic force (Newtons, N)
• $k$ = Coulomb’s constant = 8.99×1098.99 \times 10^98.99×109 Nm²/C²
• q1,q2q_1, q_2q1​,q2​ = Magnitudes of the two charges (Coulombs, C)
• $r$ = Distance between the charges (meters, m)

This force can be attractive if the charges are opposite (positive and negative) or repulsive if the charges are similar (both positive or both negative).

Concept Development: Key Points About Coulomb’s Law

1. Nature of Electrostatic Force

• The force acts along the line joining the two charges.
• It is a vector quantity, meaning it has both magnitude and direction.
• The force follows Newton’s Third Law: if charge q1q_1q1​ exerts a force on q2q_2q2​, then q2q_2q2​ exerts an equal and opposite force on q1q_1q1​.

2. Comparison with Gravitational Force

Coulomb’s Law is similar in form to Newton’s Law of Gravitation:

F=Gm1m2r2F = G \frac{m_1 m_2}{r^2}F=Gr2m1​m2​​

Where $G$ is the gravitational constant. However, there are key differences:

• Gravitational force is always attractive, whereas Coulomb’s force can be attractive or repulsive.
• Electrostatic forces are much stronger than gravitational forces at the atomic level.

For example, the electrostatic force between an electron and a proton in a hydrogen atom is about 103910^{39}1039 times stronger than the gravitational force between them.

3. The Role of Coulomb’s Constant ($k$)

The constant $k$ depends on the medium in which the charges exist. In vacuum (or air, approximately), its value is:

k=8.99×109 Nm²/C²k = 8.99 \times 10^9 \text{ Nm²/C²}k=8.99×109 Nm²/C²

However, if the charges are placed in another medium (like water), the force between them decreases due to the dielectric constant of the medium.

4. Applications of Coulomb’s Law

1. Atomic and Molecular Physics

• Coulomb’s Law explains the attraction between electrons and protons in atoms.
• It helps describe ionic bonding in chemistry, where positive and negative ions attract each other.

2. Electrical and Electronics Engineering

• It is fundamental in designing capacitors, which store charge in circuits.
• It helps in understanding electric fields and how they influence charged particles.

3. Everyday Applications

• Static electricity: The force you feel when rubbing a balloon against your hair.
• Lightning: Charged particles in clouds create a Coulomb force that leads to electrical discharge.

5. Problem-Solving Using Coulomb’s Law

Example Problem 1: Calculating Electrostatic Force

Problem:
Two charges, q1=+2.0×10−6q_1 = +2.0 \times 10^{-6}q1​=+2.0×10−6 C and q2=−3.0×10−6q_2 = -3.0 \times 10^{-6}q2​=−3.0×10−6 C, are placed 0.05 m apart. Find the force between them.

Solution:
Using Coulomb’s Law,

F=k∣q1q2∣r2F = k \frac{|q_1 q_2|}{r^2}F=kr2∣q1​q2​∣​ F=(8.99×109)(2.0×10−6)(3.0×10−6)(0.05)2F = (8.99 \times 10^9) \frac{(2.0 \times 10^{-6}) (3.0 \times 10^{-6})}{(0.05)^2}F=(8.99×109)(0.05)2(2.0×10−6)(3.0×10−6)​ F=(8.99×109)×6.0×10−120.0025F = (8.99 \times 10^9) \times \frac{6.0 \times 10^{-12}}{0.0025}F=(8.99×109)×0.00256.0×10−12​ $$F=21.6\text{ N}$$

Since the charges are opposite, the force is attractive.

Conclusion

concept development practice page 32-1 coulomb’s law is one of the most important principles in electromagnetism. It explains how charges interact and helps in understanding electric fields, forces, and potential energy in physics. Coulomb’s Law plays a critical role in science and technology, from microscopic atomic interactions to macroscopic electrical engineering applications.