Electric Charges and Fields:
Electric Charge: The word “electricity” is derived from the Greek word Elektron, which means amber. This is because the ancient Greeks noticed that rubbing amber produced static electricity. In physics, electric charge is a fundamental property of matter that determines how atoms and molecules interact. There are two types of electric charge: positive and negative. The basic rule is that like charges repel each other, while unlike charges attract. This property, known as the polarity of charge, is crucial for understanding many electrical phenomena.
Conductors and Insulators: In experiments with electric charges, it was observed that conductors and insulators behave differently. Conductors, such as metals, the Earth, and the human body, allow electric charges to flow freely through them, making them good materials for carrying electricity. On the other hand, insulators like porcelain, nylon, and wood resist the flow of electric charges, preventing electricity from passing through them. This makes insulators valuable for safety, as they protect against electrical shocks.
Properties of Electric Charge: Electric charge has three main properties:
- Quantization: The total charge on an object is an integer multiple of a basic unit of charge. This means electric charge is discrete and not continuous.
- Additivity: The total charge in a system is the algebraic sum of all individual charges. Multiple charges acting on a system combine to produce an overall charge.
- Conservation: The total charge in an isolated system remains constant. Charges can only be transferred between objects, but they cannot be created or destroyed.
Coulomb’s Law: Coulomb’s law describes the electrostatic force between two point charges. When two point charges, Q₁ and Q₂, are separated by a distance r, the magnitude of the electrostatic force F between them is given by:
- Direction of Force: The force acts along the line joining the two charges.
- Nature of Force:
- Repulsive: If both charges are of the same sign (either both positive or both negative).
- Attractive: If the charges have opposite signs (one positive and one negative).
- Conservative Nature: The electrostatic force is conservative, meaning the work done in moving a charge between two points is independent of the path taken.
- Inverse Square Law: The force between the charges decreases with the square of the distance between them.
Forces Between Multiple Charges: For multiple charges, Coulomb’s law applies to the interaction between any two charges. The net force on a charge due to multiple other charges is the vector sum of the forces exerted on it by each of the other charges. This is known as the superposition principle.
Superposition Principle: The superposition principle states that the interaction between two charges remains the same regardless of the presence of other charges in the system. This means the force between any two specific charges is unaffected by other charges nearby.
Properties of Electric Field Lines: Electric field lines have several important properties:
- Continuous Curves: Electric field lines are continuous and do not break in regions without charges. They represent the direction of the electric field at every point.
- No Intersection: Two electric field lines never cross each other, as this would imply the field has two different directions at the same point.
- Starting and Ending Points: Electric field lines start at positive charges and end at negative charges. This indicates the direction a positive test charge would move in the field.
- No Closed Loops: Unlike magnetic fields, electric field lines never form closed loops. They either start at a positive charge and end at a negative charge or extend to infinity if no negative charge is present.
Electric Flux: Electric flux measures the total number of electric field lines passing through a given area. It is calculated as:
Δθ = E · ΔS · cosθ
Where:
- E is the electric field strength,
- ΔS is the area element,
- θ is the angle between the electric field E and the normal to the area element ΔS.
Electric Dipole: An electric dipole consists of two equal and opposite charges, +q and −q, separated by a distance. The dipole moment p is calculated as:
p = q × 2a
Where:
- 2a is the distance between the charges,
- The direction of the dipole moment is from the negative charge to the positive charge.
Electric dipoles are essential in understanding how molecules and other systems interact with electric fields.
Charge on a Capacitor: A capacitor’s net charge is always zero because the charges on its two plates are equal in magnitude but opposite in sign. The charge Q on a capacitor refers to the magnitude of the charge on one of the plates.
Properties of an Ideal Battery: An ideal battery is a theoretical model that simplifies the behavior of real batteries. The key properties of an ideal battery are:
- Two Terminals: One positive and one negative.
- Constant Potential Difference: The potential difference (voltage) between the battery terminals remains constant, regardless of the load.
- Electromotive Force (emf): The potential difference between the terminals is known as the electromotive force (emf).
- Charge Conservation: The total charge in the battery is zero. If the positive terminal supplies a charge Q, the negative terminal provides an equal and opposite charge −Q.
- Work Done by the Battery: When a charge Q moves from the negative to the positive terminal, the battery does work equal to Q × E, where E is the emf of the battery.
- Symbol Representation: An ideal battery is symbolized by two parallel lines of unequal length, with the longer line representing the positive terminal and the shorter line representing the negative terminal.