Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• State and apply Coulomb's Law for charges in one dimension.
• Define and calculate electric field strength.
• Draw electric field patterns for various charge configurations.
• Explain charge quantization and conservation.
• Solve problems involving net force and net electric field.

Lesson summary

Electrostatics is the study of stationary or slow-moving electric charges. Understanding electrostatics is crucial because it explains phenomena we encounter daily, from static cling in our clothes (especially prevalent in dry climates like the Karoo) to the operation of sophisticated technologies like laser printers and electrostatic precipitators used to reduce pollution in power plants.

Furthermore, understanding electric fields is fundamental to comprehending how charged particles interact and how electrical forces are transmitted through space.

Lesson notes

Electric Charge: 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. The SI unit of electric charge is the Coulomb (C).

Charge Quantization: Electric charge is quantized, meaning it exists in discrete units. The smallest unit of charge is the elementary charge, e, which is the magnitude of the charge carried by a single proton or electron. e = 1.602 x 10 -19 C. Any observable charge is an integer multiple of this elementary charge. For example, an object can have a charge of 3.204 x 10 -19 C (2e), but it cannot have a charge of 2.5e.

Charge Conservation: Electric charge is conserved. This means 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. For example, when rubbing a plastic ruler with a woolen cloth, electrons are transferred from the wool to the ruler, making the ruler negatively charged and the wool positively charged.

However, the total charge of the ruler-wool system remains zero.

Coulomb's Law: Coulomb's Law describes the electrostatic force between two point charges. 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, it is expressed as: F = k |q 1 q 2 | / r 2 Where: F is the electrostatic force (in Newtons, N) k is Coulomb's constant (approximately 8.99 x 10 9 N·m 2 /C 2 ) q 1 and q 2 are the magnitudes of the charges (in Coulombs, C) r is the distance between the charges (in meters, m) The direction of the force is along the line joining the two charges. The force is attractive if the charges have opposite signs and repulsive if they have the same sign.

Example 1: Two point charges, q 1 = +4.0 x 10 -6 C and q 2 = -8.0 x 10 -6 C, are separated by a distance of 2.0 m. Calculate the magnitude and direction of the electrostatic force between them.

Solution: F = k |q 1 q 2 | / r 2 F = (8.99 x 10 9 N·m 2 /C 2 ) |(4.0 x 10 -6 C) (-8.0 x 10 -6 C)| / (2.0 m) 2 F = (8.99 x 10 9 ) * (3.2 x 10 -11 ) / 4 F = 0.0719 N Since the charges have opposite signs, the force is attractive. Thus, q 1 is attracted towards q 2 and q 2 is attracted towards q 1 with a force of 0.0719

N. Example 2: Three point charges are arranged in a line. Charge q 1 = +3.0 x 10 -6 C is located at x = 0 m, charge q 2 = -6.0 x 10 -6 C is located at x = 0.2 m, and charge q 3 = +2.0 x 10 -6 C is located at x = 0.5 m. Calculate the net electrostatic force on charge q 1 .

Solution: First, calculate the force between q 1 and q 2 (F 12 ): F 12 = (8.99 x 10 9 N·m 2 /C 2 ) |(3.0 x 10 -6 C) (-6.0 x 10 -6 C)| / (0.2 m) 2 F 12 = 4.0455 N (attractive, so q 1 is pulled towards q 2 , meaning positive direction) Next, calculate the force between q 1 and q 3 (F 13 ): F 13 = (8.99 x 10 9 N·m 2 /C 2 ) |(3.0 x 10 -6 C) (2.0 x 10 -6 C)| / (0.5 m) 2 F 13 = 0.21576 N (repulsive, so q 1 is pushed away from q 3 , meaning negative direction) The net force on q 1 is the vector sum of F 12 and F 13 : F net = F 12 + F 13 = 4.0455 N - 0.21576 N = 3.82974 N The net force on q 1 is 3.83 N in the positive x-direction (towards q 2 ).

Electric Field: An electric field is a region of space around a charged object in which another charged object would experience a force. The electric field strength at a point is defined as the force per unit positive charge that would be exerted on a test charge placed at that point. The SI unit of electric field strength is Newtons per Coulomb (N/C).

Mathematically: E = F / q Where: E is the electric field strength (in N/C) F is the electrostatic force (in N) q is the magnitude of the test charge (in C) The electric field due to a point charge Q at a distance r from the charge is given by: E = k * |Q| / r 2 The electric field is a vector quantity. The direction of the electric field is the direction of the force that would be exerted on a positive test charge placed in the field. Electric field lines are a useful way to visualize electric fields. The lines point in the direction of the field, and the density of the lines indicates the strength of the field. Electric field lines originate on positive charges and terminate on negative charges.

Example 3: A point charge of +5.0 x 10 -6 C is placed at the origin. Calculate the magnitude and direction of the electric field at a point 3.0 m to the right of the charge.

Solution: E = k * |Q| / r 2 E = (8.99 x 10 9 N·m 2 /C 2 ) * |5.0 x 10 -6 C| / (3.0 m) 2 E = (8.99 x 10 9 ) * (5.0 x 10 -6 ) / 9 E = 4994.44 N/C Since the source charge is positive, the electric field points away from the charge (to the right in this case). Thus, the electric field at the point is 4994.44 N/C to the right.