Electrostatics and Electric Circuit Study Notes
ELECTROSTATICS AND ELECTRIC CIRCUIT
Learning Outcomes
By the end of this section, students will be able to:
Calculate the electric field resulting from a point charge.
Determine the magnitude and direction of the electric force among any point charges.
Acquire knowledge and understanding in electrostatic phenomena.
Demonstrate an understanding of the components and functions of electrical circuits commonly found at home and in the workplace.
Construct and analyze simple electrical circuits using schematic diagrams, and work with electrical tools and components while examining everyday electrical devices and appliances.
Define a capacitor and explain some of its applications in daily life.
Apply Kirchhoff’s rules to solve circuit problems.
6.1 Coulomb’s Law
Objectives
State Coulomb’s law.
Calculate the magnitude and direction of electric force between any two charges.
Solve problems involving Coulomb’s law.
Explain Coulomb’s law using the concept of vectors.
Explain the meaning of a coulomb.
Brainstorming Questions
What are the compositions of an atom?
What are the two types of charges and their origin?
How can a body be charged positively and negatively?
What does the law of electrostatics say?
Properties of Electric Charges
Electric charges have specific properties:
Property I: Like charges repel and unlike charges attract each other.
Property II: Electric charge is always conserved; the number of electrons gained by one object equals the number lost by another.
Property III: Electric charge is quantized, implying that charge (q) always occurs as an integral multiple of the charge of an electron, represented as:
q = n e = ext{±} ext{ (where } n = 1, 2, 3, … ext{)}
where e = 1.6 imes 10^{-19} ext{ C}.
Thus:
1e^{-} = - 1.6 imes 10^{-19} ext{ C} (electron)
1e^{+} = 1.6 imes 10^{-19} ext{ C} (proton)
Example - Charge Calculation
Example 6.1: What number of protons are needed to create a charge of +1.0 C?
Solution: Given:
Charge q = 1.0 ext{ C},
Charge of a proton e = 1.6 imes 10^{-19} ext{ C},
To find the number of protons:
n_{ ext{protons}} = rac{q}{e} = rac{1.0 ext{ C}}{1.6 imes 10^{-19} ext{ C}} ext{ } = 6.25 imes 10^{18} ext{ protons}.
Similarly, the number of electrons needed to create a charge of -1.0 C is also:
n = rac{1.0 ext{ C}}{1.6 imes 10^{-19} ext{ C}} = 6.25 imes 10^{18} ext{ electrons}.
6.2 Electric Fields
Objectives
Define electric fields and electric flux.
Sketch electric field lines.
Solve problems involving electric fields.
Map electric field line patterns using electric lines of force.
Calculate the magnitude and direction of the electric field due to a point charge and multiple point charges.
Properties of Electric Field Lines
Electric field lines exhibit the following characteristics:
They do not cross each other.
They commence from positive charges and radiate toward negative charges where they terminate.
They are always perpendicular to the surface of the charged body.
The density of lines indicates the strength of the electric field; closer lines represent a stronger field.
Equally spaced lines reflect a uniform field.
Electric Field Strength Equation
The electric field strength E can be defined as:
E = rac{F}{q},
where F is the force experienced by the charge q.
Example - Electric Field Calculation
Example 6.4: Calculate the strength of the electric field E due to a point charge of 2.0 nC at a distance of 5.0 mm from it.
Solution: Use the equation:
E = rac{F}{q} = rac{k imes |Q|}{r^2},
where k = 9 imes 10^9 ext{ N m}^2/ ext{C}^2 and the distance must be converted to meters.
6.3 Electric Potential
Objectives
Define electric potential, equipotential surfaces, and solve related problems.
Explain concepts of volts, potential difference, and emf.
Electric Potential Energy Definition
Electric potential energy is defined in terms of the work done to move a charge within an electric field:
U = k rac{Qq}{r}, where:k is the Coulomb's constant,
Q is the source charge,
q is the test charge,
r is the distance between the charges.
Electric Potential Formula
Electric potential V is given by:
V = rac{U}{q} = k rac{Q}{r}.
Example - Potential Calculation
Example 6.7: Determine the electric potential produced by a 1μC charge at 1 mm distance.
Solution: Plug into the formula:
V = k rac{Q}{r} = rac{(9 imes 10^9) imes (1 imes 10^{-6})}{0.001} = 9 imes 10^{3} ext{ volts}.
6.4 Electric Current, Resistance, and Ohm's Law
Objectives
Define electric current, current density, resistance, and related concepts.
Explain the effects of connecting light bulbs in series versus parallel circuits.
Electric Current Definition
Electric current (I) is the flow of electric charge, measured in Amperes (A).
Ohm’s Law
Ohm’s Law states that V = IR, where:
V = Voltage,
I = Current,
R = Resistance.
Resistance and Conductivity Definition
Resistance represents the opposition to current flow in a conductor:
R = rac{V}{I}.
Example - Resistance Calculation
Example 6.11: Calculate the resistance of an automobile headlight with a current of 2.50 A when 12.0 V is applied:
R = rac{V}{I} = rac{12 ext{ V}}{2.5 ext{ A}} = 4.8 ext{ Ω}.
6.6 Capacitors and Capacitance
Objectives
Define capacitors, capacitance, and effects of inserting dielectrics.
Calculate capacitance for various configurations.
Capacitor Definition
A capacitor is a device for storing electric charge and energy.
Capacitance Formula
C = rac{Q}{V}, where:
C = Capacitance,
Q = Charge stored,
V = Voltage across the plates of the capacitor.
Example - Capacitance Calculation
Example 6.20: Determine the effects of inserting a dielectric in an isolated capacitor:
Capacitance increases,
Potential difference decreases,
Charge stored remains the same.
6.7 Electric Circuits in Our Surroundings
Objectives
Apply knowledge of electric circuits to household electric installations.
Summary
Electric charges are quantized, and Coulomb's Law expresses the electrostatic force's relationship with distance and charge. Electric currents, resistance, and capacitance are fundamental principles relevant in household electric circuits, influencing how devices and appliances operate efficiently.
Exercises
Define key concepts and calculate using given problems regarding electric charges, potentials, currents, resistances, and circuits.