Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Define electric charge and electric fields.
• State and apply Coulomb's Law to calculate electrostatic force.
• Calculate the net electric field at a point.
• Describe electric fields using field lines.
• Understand electric potential difference and conservation of charge.

Lesson summary

This week, we delve into the fascinating world of electrostatics and electric fields. Understanding how stationary electric charges interact is fundamental to understanding everything from lightning to how photocopiers work. In South Africa, where access to reliable electricity is often a challenge, understanding the principles behind electrical phenomena is crucial for innovation in sustainable energy solutions, responsible use of resources, and even understanding the impact of electrical storms on infrastructure. From the charging of cellphones (a ubiquitous technology) to large-scale power distribution, electrostatics plays a crucial, albeit often unseen, role.

Lesson notes

Electric Charge (q): Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field.

There are two types of electric charge: positive and negative. Like charges repel each other, and unlike charges attract each other. The SI unit of electric charge is the coulomb (C). The smallest unit of charge that can exist freely is the elementary charge, e, which is the magnitude of the charge of a single proton or electron (e = 1.6 x 10 -19 C). Electrons have a negative charge (-e), and protons have a positive charge (+e).

Electric Field (E): An electric field is a region of space around an electrically charged object in which another charged object will experience a force. It is a vector quantity, meaning it has both magnitude and direction. The direction of the electric field at a point is the direction of the force that a positive test charge would experience if placed at that point. Electric fields are represented by electric field lines, which show the direction of the electric field at each point.

Electric Field Lines: Originate on positive charges and terminate on negative charges (or extend to infinity). The density of field lines indicates the strength of the electric field (more lines = stronger field). Field lines never cross. Field lines are perpendicular to the surface of the charged object.

Electric Field Strength (E): Electric field strength is defined as the force per unit charge experienced by a positive test charge placed at a point in the electric field. Mathematically, it is expressed as: E = F/q where: E is the electric field strength (N/C or V/m) F is the electrostatic force (N) q is the magnitude of the test charge (C)

Coulomb's Law: Coulomb's Law describes the electrostatic force between two point charges. The law states that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.

Mathematically: F = k (q 1 q 2 ) / r 2 where: F is the electrostatic force (N) k is Coulomb's constant (k ≈ 8.99 x 10 9 N⋅m 2 /C 2 ) q 1 and q 2 are the magnitudes of the charges (C) r is the distance between the charges (m) Important Considerations for Coulomb's Law: The force is attractive if the charges have opposite signs and repulsive if the charges have the same sign. The force is a vector quantity, so direction is important. The force acts along the line joining the two charges. Coulomb's Law applies only to point charges (charges whose size is negligible compared to the distance between them).

Net Electric Field: When multiple charges are present, the net electric field at a point is the vector sum of the electric fields due to each individual charge. This requires resolving electric field vectors into components (x and y components), adding the components separately, and then finding the magnitude and direction of the resultant vector. Electric Potential Difference (ΔV): Electric potential difference (also known as voltage) is the work done per unit charge to move a positive test charge between two points in an electric field.

Mathematically: ΔV = W/q where: ΔV is the electric potential difference (V) W is the work done (J) q is the magnitude of the charge (C) Relationship between Electric Field and Potential Difference: For a uniform electric field, the electric potential difference is related to the electric field strength by: ΔV = -E * d where: d is the distance between the two points in the direction of the electric field. The negative sign indicates that the electric potential decreases in the direction of the electric field.

Conservation of Charge: The principle of conservation of charge states that the total electric charge in an isolated system remains constant. Charge can be transferred from one object to another, but it cannot be created or destroyed. When two identical conducting spheres are brought into contact and then separated, the charge is shared equally between them.

Worked example

Example 1: Coulomb's Law

Two point charges, q 1 = +4 μC and q 2 = -8 μC, are separated by a distance of 60 mm. Calculate the magnitude and direction of the electrostatic force between them.

Solution:

Convert units: q 1 = 4 x 10 -6 C, q 2 = -8 x 10 -6 C, r = 0.06 m

Apply Coulomb's Law:

F = (8.99 x 10 9 N⋅m 2 /C 2 ) (4 x 10 -6 C 8 x 10 -6 C) / (0.06 m) 2

F = 8.99 x 10 9 * 32 x 10 -12 / 0.0036

F = 0.08 N

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

Therefore, q 1 experiences a force towards q 2 and q 2 experiences a force towards q 1 .

Example 2: Net Electric Field