Lesson Note on Electric Field: Coulomb’s Law and Electric Field Intensity for SSS 2

Class: Senior Secondary School 2 (SS2 / SSS2)
Term: 3rd Term
Week: 3
Age: 16 years
Duration: 45 minutes
Subject: Physics
Curriculum Theme: Fields
Previous Lesson: Electric Field: Gas Conduction, Thermionic Emission and Diode Valve.
Topic: ELECTRIC FIELD
Subject Matter: Electric force between point charges Coulomb’s law (inverse square law), concept of electric field (force per unit charge idea), electric field intensity (definition and units), electric potential (work done per unit charge)

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

• Define electric force and state Coulomb’s law.
• Explain the concept of electric field.
• Define electric field intensity and electric potential.
• Compare electric force with gravitational force qualitatively.

Affective Domain:

• Appreciate the significance of electric fields in various applications.
• Develop interest in studying electromagnetism.

Psychomotor Domain:

• Calculate electric force between point charges using Coulomb’s law.
• Solve problems involving electric field intensity.
• Solve problems involving electric potential.

Social Domain:

• Collaborate effectively with peers to solve physics problems.

Reference Materials

The following resources were used in planning this lesson:

• Senior Secondary Schools Education Curriculum
• State Unified Scheme of Work
• New School Physics by M.W. Anyakoha
• https://www.waecdirect.org/curriculum/physics_sss.pdf
• https://www.britannica.com/science/electric-field

Instructional Materials

The teacher will teach this lesson with the aid of:

• Physics textbook
• Charts illustrating electric field lines
• Equipped laboratory (for potential future demonstrations)
• Calculators

Rationale for the Lesson

Understanding electric fields helps pupils grasp how charges interact and how forces are transmitted through space. This knowledge is fundamental to understanding many electrical devices and natural phenomena, and it lays the groundwork for advanced topics in electromagnetism.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of basic concepts of electric charge, types of forces, work, and energy from previous lessons.

Lesson Content/Board Summary

ELECTRIC FIELD

Electric Force between Point Charges (Coulomb’s Law)

Electric force is the attractive or repulsive force between two charged objects. Like charges repel, and unlike charges attract.

Coulomb’s Law states that the electric force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between their centers.

Mathematically, Coulomb’s law is given by:

F = k * (q₁q₂) / r²

• F = Electric force (Newtons, N)
• q₁, q₂ = Magnitudes of the point charges (Coulombs, C)
• r = Distance between the centers of the charges (meters, m)
• k = Coulomb’s constant, approximately 9 x 10⁹ Nm²/C²

The constant k can also be expressed as k = 1 / (4πε₀), where ε₀ is the permittivity of free space (8.85 x 10⁻¹² C²/Nm²).

Worked Example 1: Calculating Electric Force

Calculate the electric force between two point charges of +3 μC and -4 μC placed 0.2 m apart in a vacuum.

Step 1: Identify given values and formula.

• q₁ = +3 μC = 3 x 10⁻⁶ C
• q₂ = -4 μC = -4 x 10⁻⁶ C
• r = 0.2 m
• k = 9 x 10⁹ Nm²/C²
• Formula: F = k * |q₁q₂| / r² (use absolute value for force magnitude)

Step 2: Substitute values into the formula.

F = (9 x 10⁹ Nm²/C²) * |(3 x 10⁻⁶ C) * (-4 x 10⁻⁶ C)| / (0.2 m)²

F = (9 x 10⁹) * (12 x 10⁻¹²) / (0.04)

Step 3: Calculate the force.

F = (108 x 10⁻³) / 0.04

F = 2.7 N

Since the charges are of opposite signs, the force is attractive.

Worked Example 2: Finding Charge

Two identical point charges exert a repulsive force of 0.09 N on each other when they are 10 cm apart. Calculate the magnitude of each charge.

Step 1: Identify given values and rearrange formula.

• F = 0.09 N
• r = 10 cm = 0.1 m
• k = 9 x 10⁹ Nm²/C²
• q₁ = q₂ = q
• From F = k * q² / r², we get q² = F * r² / k

Step 2: Substitute values.

q² = (0.09 N) * (0.1 m)² / (9 x 10⁹ Nm²/C²)

q² = (0.09) * (0.01) / (9 x 10⁹)

q² = 0.0009 / (9 x 10⁹)

q² = 1 x 10⁻¹³ C²

Step 3: Calculate q.

q = √(1 x 10⁻¹³) = √(10 x 10⁻¹⁴)

q ≈ 3.16 x 10⁻⁷ C

The magnitude of each charge is approximately 3.16 x 10⁻⁷ C.

Comparison of Electric Force and Gravitational Force

Similarities:

• Both are inverse square law forces (force is inversely proportional to the square of the distance).
• Both act over a distance without direct contact.

Differences:

• Nature of Force: Electric force can be attractive or repulsive, while gravitational force is always attractive.
• Mediating Property: Electric force acts between charges, while gravitational force acts between masses.
• Strength: Electric force is significantly stronger than gravitational force. For elementary particles like protons, the electric force is about 10³⁶ times stronger than the gravitational force.

Concept of Electric Field

An electric field is a region around a charged object where another charged object would experience an electric force. It is a vector field, meaning it has both magnitude and direction at every point in space.

Electric field lines are used to visualize electric fields:

• They originate from positive charges and terminate on negative charges.
• The density of the lines indicates the strength of the field (closer lines mean a stronger field).
• They never cross each other.
• The direction of the field line at any point indicates the direction of the force a positive test charge would experience.

Electric Field Intensity (E)

Electric field intensity (also called electric field strength) at a point is defined as the electric force experienced per unit positive test charge placed at that point.

Mathematically:

E = F / q₀

Where:

• E = Electric field intensity (Newtons per Coulomb, N/C, or Volts per meter, V/m)
• F = Electric force (N)
• q₀ = Positive test charge (C)

For a point charge Q, the electric field intensity at a distance r from it is:

E = k * Q / r²

Worked Example 3: Calculating Electric Field Intensity

A point charge of +5 μC creates an electric field. Calculate the electric field intensity at a point 0.5 m away from the charge.

Step 1: Identify given values and formula.

• Q = +5 μC = 5 x 10⁻⁶ C
• r = 0.5 m
• k = 9 x 10⁹ Nm²/C²
• Formula: E = k * Q / r²

Step 2: Substitute values into the formula.

E = (9 x 10⁹ Nm²/C²) * (5 x 10⁻⁶ C) / (0.5 m)²

E = (45 x 10³) / 0.25

Step 3: Calculate E.

E = 180 x 10³ N/C = 1.8 x 10⁵ N/C

The electric field intensity is 1.8 x 10⁵ N/C, directed away from the positive charge.

Electric Potential (V)

Electric potential at a point in an electric field is defined as the work done per unit positive test charge in bringing the test charge from infinity to that point without acceleration.

Mathematically:

V = W / q₀

Where:

• V = Electric potential (Volts, V, or Joules per Coulomb, J/C)
• W = Work done (Joules, J)
• q₀ = Positive test charge (C)

For a point charge Q, the electric potential at a distance r from it is:

V = k * Q / r

Worked Example 4: Calculating Electric Potential

Calculate the electric potential at a point 0.3 m away from a point charge of +2 nC.

Step 1: Identify given values and formula.

• Q = +2 nC = 2 x 10⁻⁹ C
• r = 0.3 m
• k = 9 x 10⁹ Nm²/C²
• Formula: V = k * Q / r

Step 2: Substitute values into the formula.

V = (9 x 10⁹ Nm²/C²) * (2 x 10⁻⁹ C) / (0.3 m)

V = 18 / 0.3

Step 3: Calculate V.

V = 60 V

The electric potential at that point is 60 Volts.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher reviews the concept of electric charge and the interaction between charges, asking pupils what happens when two positive charges are brought close together.
Pupils’ Activity: Pupils respond by stating that like charges repel and unlike charges attract.
Learning Point: Pupils recall prior knowledge about electric charges and their interactions.

Step 2: Electric Force and Coulomb’s Law

Time: 8 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher introduces the concept of electric force and states Coulomb’s Law, writing the formula F = k * (q₁q₂) / r² on the board and explaining each variable and its unit.
Pupils’ Activity: Pupils listen attentively, copy the formula, and ask questions for clarification.
Learning Point: Pupils understand the definition and mathematical representation of Coulomb’s Law.

Step 3: Worked Examples on Coulomb’s Law

Time: 8 minutes
Teaching Skill: Problem Solving/Guided Practice
Teacher’s Activity: The teacher solves worked examples on the board, demonstrating how to calculate electric force between point charges and how to find unknown charges, guiding pupils through each step.
Pupils’ Activity: Pupils follow the steps, copy the examples, and attempt to solve similar problems.
Learning Point: Pupils develop problem-solving skills for calculating electric force.

Step 4: Comparison with Gravitational Force

Time: 5 minutes
Teaching Skill: Comparative Analysis
Teacher’s Activity: The teacher leads a discussion comparing electric force with gravitational force, highlighting their similarities (inverse square law) and key differences (strength, nature).
Pupils’ Activity: Pupils contribute to the discussion, identifying the similarities and differences between the two forces.
Learning Point: Pupils understand the distinct characteristics of electric and gravitational forces.

Step 5: Electric Field Intensity

Time: 6 minutes
Teaching Skill: Definition/Explanation
Teacher’s Activity: The teacher introduces the concept of an electric field and defines electric field intensity (E = F/q₀ = kQ/r²), explaining its units and direction using field lines.
Pupils’ Activity: Pupils listen, take notes, and ask questions about the concept and formula.
Learning Point: Pupils grasp the definition and formula for electric field intensity.

Step 6: Electric Potential

Time: 6 minutes
Teaching Skill: Definition/Explanation
Teacher’s Activity: The teacher defines electric potential (V = W/q₀ = kQ/r), explaining it as work done per unit charge and stating its units.
Pupils’ Activity: Pupils write down the definition and formula for electric potential.
Learning Point: Pupils understand the concept and formula for electric potential.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. State Coulomb’s Law.
2. Calculate the electric force between two charges of +2 C and -3 C separated by 1 meter.
3. Define electric field intensity and state its unit.
4. What is electric potential? State its unit.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the main points of the lesson, emphasizing the formulas for electric force, field intensity, and potential. The teacher also assigns homework.
Pupils’ Activity: Pupils listen to the summary and copy down the assigned homework.
Learning Point: Pupils consolidate their understanding of electric fields and related concepts.

Lesson Keywords

• Electric force – The attractive or repulsive force between charged objects.
• Coulomb’s law – Describes the electric force between two point charges.
• Electric field – A region around a charged object where another charge experiences a force.
• Electric field intensity – Force per unit positive test charge.
• Electric potential – Work done per unit positive test charge to bring it from infinity to a point.
• Point charge – A hypothetical charge concentrated at a single point in space.
• Permittivity – A measure of the opposition offered by a medium to the formation of an electric field.

Differentiation

For pupils who grasp concepts quickly, the teacher can provide more complex problems involving multiple charges or ask them to research real-world applications of electric fields. For pupils needing more support, the teacher will provide simplified examples and one-on-one guidance, focusing on understanding the basic definitions and single-step calculations.

Note for teachers using this lesson plan

Ensure that pupils have a solid understanding of basic algebra for solving the formulas. Use visual aids like diagrams of electric field lines to help pupils conceptualize the invisible field. Where possible, demonstrate simple electrostatic phenomena using charged rods and pith balls to make the concepts more tangible.