Physics Electric Charge and Electricity Exam Notes

Definition: An electrically charged object is known as a charged object or an electric charge.
Symbols: Electric charge is represented by the symbols q or Q.
Units: The unit of electric charge is Coulomb (C).
- Common subunits include:
- 1 mC = $10^{-3} C$ (milli)
- 1 µC = $10^{-6} C$ (micro)
- 1 nC = $10^{-9} C$ (nano)
- 1 pC = $10^{-12} C$ (pico)
Charged Objects: Electrically charged objects can attract light objects.
Types of Charge: There are two types of electric charge:
- Positive charge
- Negative charge

Definition: A point charge is an electrically charged object whose size is very small compared to the distance from it to the point being studied.
Interactions:
- Like charges repel each other.
- Opposite charges attract each other.
Interaction Force: The force between two point charges is called the interaction force, which obeys the following characteristics:
- Direction: Force acts along the line connecting the two point charges.
- Magnitude: It is directly proportional to the product of the magnitudes of the two charges and inversely proportional to the square of the distance between them.

Formula: The electric force F between two point charges can be expressed as: F = k rac{|q1 q2|}{r^2} , where:
- k: Coulomb's constant, $9 imes 10^9 ext{ (N m²/C²)}$
- ε: Permittivity of the medium (For vacuum or air, ε = 1).

Definition: The electric field is the region around a charge where it exerts a force on other charges. Electric fields produce electric forces on charges placed within them.
Characteristics of Electric Field:
- When a charge q is placed in an electric field, it experiences a force.
- This force can either attract or repel, depending on the sign of the charges.

Definition: The intensity of the electric field at a point is a measure of the force it exerts on a unit positive charge placed at that point.
Vector Representation: Electric field intensity vector E can be represented in two ways:
1. Directly by the source charge Q at point M (distance r away).
2. By placing a test charge q at point M and observing the force on it.
Electric Field Intensity Formula: Magnitude is given by,
E = k rac{|Q|}{r^2} ,
where E is measured in V/m.

The direction of the electric field vector E is:
- Away from the positive charge (if Q > 0)
- Toward the negative charge (if Q < 0)
Magnitude:
E = rac{F}{q}
where F is the electric force experienced by charge q.

Definition: Electric field lines are curves drawn in space such that at any point, the tangent to the line represents the direction of the electric field at that point.
Key Characteristics:
- There is exactly one electric field line through any given point in the field.
- Electric field lines never cross.
- The lines point away from positive charges and toward negative charges.
- For static electric fields, the lines are open and do not form closed loops.
- The density of lines indicates the strength of the field: denser lines correspond to stronger electric fields.

An electric field is said to be uniform if the electric field intensity vector E has the same magnitude and direction at every point in the field.
Characteristics: In a uniform electric field (such as between two parallel plates), field lines are straight, parallel, and evenly spaced.

Electric Field Strength: E = rac{U}{d} , where:
- U is the potential difference between two plates (V).
- d is the separation between the plates (m).

When a charge q moves through an electric field, it experiences an electric force given by: F = qE .
- Positive charges move in the direction of the electric field,
- Negative charges move opposite to the electric field direction.

The work done by the electric force as a charge moves from point M to point N in a uniform electric field is given by: W_{MN} = qEd , where:
- E is the electric field strength,
- d is the displacement in the direction of the field.

The electric potential at point M in an electric field is defined as the amount of work done in bringing a unit charge from infinity to point M:
VM = rac{WM}{q} ,
Unit: The unit of electric potential (voltage) is the Volt (V).

The change in electric potential energy as a charge moves from M to N is given by:
WM - WN = A_{MN}.

Definition: A capacitor is a device composed of two conductive plates separated by an insulator, used to accumulate and discharge electric energy.
Charging: It can be charged by connecting its plates to a voltage source, gaining equal but opposite charges.
Capacitance ($C$): Capacity of a capacitor to store charge, defined as: C = rac{Q}{U} , where:
- Q is the charge stored,
- U is the voltage across the plates.
Unit: Capacitance is measured in Farads (F).

The energy ($W$) stored in a capacitor is given by:
W = rac{1}{2} Q U = rac{1}{2} C U^2 = rac{Q^2}{2C} .

Definition: Electric current is the directed flow of electric charge.
Direction: Conventional current direction is from positive to negative (positive charge movement).
Current Measurement: Measured in Amperes (A) using an ammeter.

Formula: The current is defined by: I = rac{ ext{Δ}q}{ ext{Δ}t}, where:
- Δq is the charge in coulombs,
- Δt is the time in seconds.

Definition: Resistance ($R$) is the opposition to the flow of current in a conductor: R = rac{U}{I}, where:
- U is the voltage,
- I is the current.
Units: The unit of resistance is Ohms (Ω).

Power: The electric power consumed by a circuit is the rate at which energy is used, defined as: P = U I = rac{W}{t}, where:
- P is power (Watts),
- U is voltage (Volts),
- I is current (Amperes).
Energy Loss: The heat generated in a resistor due to current flow is given by:
Q= R I^2 t.

Understanding electric charge, field, potential, current, and associated laws is crucial in physics and electrical engineering.