PHY 102 General Physics II: Comprehensive Notes on Forces and Electrostatics

Introduction to General Physics II and the Nature of Force

These lecture notes represent the official curriculum for PHY 102: General Physics II at Olabisi Onabanjo University, Department of Physics, as prepared by Dr. A. T. Talabi. The course encompasses fundamental concepts in classical mechanics and electromagnetism, specifically focusing on forces in nature, electrostatics, Coulomb's law, superposition, and electric fields and potential.

A force is scientifically defined as a push or pull acting upon an object resulting from its interaction with another object. Forces are responsible for changing an object’s speed, direction, or physical shape. In physics, force is categorized as a vector quantity because it possesses both magnitude (size) and direction. The SI unit of force is the Newton ( $N$ ), named after the English scientist Sir Issac Newton.

One Newton ( $1\,N$ ) of force is defined as the magnitude of force required to accelerate a mass of $1\,kg$ by $1\,m/s^2$ in the direction of the applied force. In the study of science, forces are broadly classified into two categories: contact forces and non-contact forces (also referred to as fundamental forces).

Classification of Contact Forces

Contact forces are those applied to objects only through direct physical touching. These forces represent the physical interaction between two objects where one object exerts a force on the other. Common examples include the stretching of a spring balance, the pushing of a cow, kicking a football, pushing a door, or hitting a ball.

Applied Force ( $F_A$ ) is a specific type of contact force exerted when a person or object pushes or pulls another object. It requires direct physical contact and can change the motion or direction of the object. Like all forces, it is measured in Newtons ( $N$ ) and acts in the direction of the applied push or pull.

Normal Force ( $F_N$ ) is the force a surface exerts on an object in contact with it. It acts perpendicular to the surface and provides the support necessary to prevent the object from passing through the surface. The normal force is a result of an action–reaction interaction and helps balance other forces acting vertically on the object.

Frictional Force ( $F_f$ ) is a contact force that opposes the motion of an object moving over a surface. It acts parallel to the surface and always in the opposite direction of the motion. Friction arises from the roughness or microscopic interaction between two surfaces in contact. It is essential for daily activities such as walking, gripping objects, and stopping moving bodies.

Non-Contact forces and Newton's Law of Universal Gravitation

Non-contact forces act between objects without any physical contact, operating through fields over a distance. Major examples include gravitational, magnetic, and electrostatic forces. These forces influence objects even when they are separated by significant distances.

Gravitational force is a non-contact, attractive force that exists between any two objects possessing mass. It always pulls bodies toward each other. Gravity specifically refers to the attraction between the Earth and objects near its surface. Despite being the weakest of the four fundamental forces, it acts over an infinite distance. The force is described by Newton’s Law of Universal Gravitation, which states that the gravitational force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them:

$F = G \frac{m_1 \times m_2}{r^2}$

In this equation, $G$ represents the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between their centers.

Magnetic force is another non-contact force exerted by a magnet on other magnetic substances. For instance, if a magnet is brought near an iron nail, the magnet exerts a force that pulls the nail toward it.

Electrostatic Force and Principles of Electrostatics

Electrostatic force is the force of attraction or repulsion between electrically charged particles, acting between positive and negative charges. Unlike charges attract, while like charges repel. This force follows Coulomb’s law, meaning it is proportional to the product of the charges and inversely proportional to the square of the distance between them. Electrostatic force is significantly stronger than gravitational force and operates over a long range.

Electrostatics is the specialized branch of physics dealing with electric charges at rest and the forces between them. It involves studying how charged objects interact, how electric fields are formed, and how these charges influence their surroundings. Electrostatic effects are frequently observed when materials are charged via friction, conduction, or induction.

Electric charge is a fundamental property of matter. Charges are classified into two types: positive charges ( $+$ ), carried by protons, and negative charges ( $-−$ ), carried by electrons. Key properties of electric charge include the fact that like charges repel, unlike charges attract, and charge is always conserved (it cannot be created or destroyed, only transferred). The SI unit of charge is the coulomb ( $C$ ).

Newton's Laws of Motion

Newton's First Law (Law of Inertia) states that an object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction, unless acted upon by an unbalanced force. Effectively, if no force acts on a body, its velocity remains constant.

Newton's Second Law establishes a relationship between the net force ( $F$ ) acting on a mass ( $m$ ) and its acceleration ( $a$ ). Experiments demonstrate that mass is a measure of how motion is influenced by forces. Acceleration is directly proportional to the net force and inversely proportional to mass, expressed as:

$F = ma$

Newton's Third Law (Action-Reaction) states that for every action, there is an equal and opposite reaction. When considering two objects $A$ and $B$ , the force object $A$ exerts on object $B$ ( $F_{AB}$ ) is equal in magnitude and opposite in direction to the force object $B$ exerts on object $A$ ( $F_{BA}$ ):

$F_{AB} = -F_{BA}$

Methods of Charging Bodies

Objects can become electrically charged through three primary methods: friction, induction, and conduction.

Charging by Friction occurs when two neutral insulating materials are rubbed together. Electrons transfer from the material with lower electron affinity to the one with higher affinity, resulting in both materials becoming charged.

Charging by Induction is the process of charging a neutral conductor without direct physical contact. This occurs due to the redistribution of charges within the conductor when a charged body is brought nearby. The specific steps are:

Bring a charged object close to a neutral conductor without touching it.
Allow the internal charges to rearrange due to the external electric field.
Connect the conductor to the ground (earth) to allow electron flow.
Remove the grounding connection while the charged object is still nearby.
Finally, remove the charged object.

Charging by Conduction involves the transfer of charge between two conductors through direct physical contact. This results in both objects sharing the same type of charge (either both positive or both negative).

Numerical Problems and Solutions

Problem 2: A charge of $2\,C$ moves with a velocity of $3\,m/s$ perpendicular to a magnetic field of $0.5\,T$ . Calculate the magnetic force acting on the charge.

$F = qvB$

Given: $q = 2\,C$ , $v = 3\,m/s$ , $B = 0.5\,T$

$F = 2 \times 3 \times 0.5$

$F = 3\,N$

Problem 3: A straight wire of length $0.4\,m$ carrying a current of $5\,A$ is placed perpendicular to a magnetic field of $0.2\,T$ . Calculate the magnetic force on the wire.

$F = BIL$

Given: $B = 0.2\,T$ , $I = 5\,A$ , $L = 0.4\,m$

$F = 0.2 \times 5 \times 0.4$

$F = 0.4\,N$

Note: The transcript lists Problem 1, Problem 4, and Problem 5 as situational headings or placeholders without accompanying text or calculations.

Questions & Discussion

Question: Why don’t we feel gravitational attraction between two students sitting together?

Answer: We do not feel gravitational attraction between two students sitting together because the gravitational force between them is extremely small. There are four primary reasons why this force is unnoticeable:

Very small masses: Humans have very small masses compared to planetary bodies.
Very small gravitational constant: The value of $G$ is extremely small.
Dominance of Earth's gravity: Earth’s gravity is much stronger and dominates the human experience.
Friction: Friction between the students and their chairs or the floor prevents any tiny motion that might result from the attraction.