Understanding Electric Charge

• Electric charge is a fundamental property causing matter to experience force in an electromagnetic field.
• Electric charge is conserved; the total electric charge in an isolated system remains constant.
• Electric charge is quantized, existing in discrete units that are integer multiples of the elementary charge.
• Elementary charge is the magnitude of the charge carried by a single proton or electron.
• Electric charge comes in two types: positive and negative.
• Like charges repel, while opposite charges attract.
• The SI unit of electric charge is the coulomb (C).

Properties of Electric Charge

• Electric charge is quantized, existing in integer multiples of the elementary charge (e ≈ 1.602 × 10-19 C).
• Conservation of electric charge means that the total electric charge in an isolated system remains constant.
• Charge can be transferred but not created or destroyed.
• Additivity of electric charges means the total charge of a system is the algebraic sum of all individual charges.
• Electric charge is transferable from one object to another through contact or other methods.
• Invariance of electric charge means that the magnitude of electric charge is independent of the velocity of the charged body.

Charging Objects

• Charging by friction (triboelectric effect) involves transferring electrons between two neutral objects when rubbed together.
• One object gains electrons and becomes negatively charged through friction.
• The other object loses electrons and becomes positively charged through friction.
• Charging by conduction involves transferring charge between two objects in direct contact.
• Electrons flow from an object with excess electrons to one with a deficit until they reach the same electric potential during conduction.
• Charging by induction is the redistribution of charges within an object due to a nearby charged object without direct contact.
• Grounding is connecting an object to the Earth, which acts as a large reservoir of electric charge and can neutralize charged objects.

Coulomb's Law

• Coulomb's Law quantifies the electrostatic force between two point charges.
• The force is directly proportional to the product of the magnitudes of the charges.
• The force is inversely proportional to the square of the distance between the charges.
• The force is attractive if the charges have opposite signs and repulsive if the charges have the same sign.
• Coulomb's Law is expressed mathematically as F = k * |q1 * q2| / r^2.
• F represents the electrostatic force.
• k is Coulomb's constant (approximately 8.9875 × 10^9 N⋅m^2/C^2).
• q1 and q2 are the magnitudes of the charges.
• r is the distance between the charges.

Electric Fields

• An electric field is a region of space around a charged object in which another charged object experiences an electric force.
• Electric field strength (E) is defined as the force per unit charge experienced by a small positive test charge placed in the field: E = F / q.
• E is the electric field strength measured in N/C.
• F is the electric force measured in N.
• q is the test charge measured in C.
• Electric field lines visually represent the electric field, indicating the field's direction and strength.
• Electric field lines originate from positive charges and terminate on negative charges.
• The density of electric field lines indicates the strength of the electric field.
• Closer lines indicates a stronger field.

Electric Potential

• Electric potential (V) is the electric potential energy per unit charge at a location in an electric field.
• The electric potential difference (ΔV) between two points is the work done per unit charge to move a charge between those points.
• The SI unit of electric potential is the volt (V), with 1 V = 1 J/C.
• Electric potential is a scalar quantity.
• Equipotential surfaces are surfaces on which the electric potential is constant.
• Electric field lines are always perpendicular to equipotential surfaces.

Conductors, Insulators, and Semiconductors

• Conductors allow electric charge to move freely through them (e.g., metals).
• Insulators do not allow electric charge to move freely through them (e.g., rubber, glass).
• Semiconductors have electrical conductivity between that of conductors and insulators (e.g., silicon, germanium).
• In conductors, electric charge resides on the surface of the material.
• In electrostatic equilibrium, the electric field inside a conductor is zero.

Electric Dipole

• An electric dipole consists of two equal and opposite charges (+q and -q) separated by a small distance (d).
• The dipole moment (p) is a vector quantity defined as p = q * d.
• p is the dipole moment measured in C⋅m.
• q is the magnitude of the charge measured in C.
• d is the distance vector from the negative charge to the positive charge measured in m.
• An electric dipole experiences torque in a uniform electric field.
• The torque tends to align the dipole moment with the field.
• The torque (τ) on an electric dipole in a uniform electric field is given by τ = p × E.
• τ is the torque measured in N⋅m.
• p is the dipole moment measured in C⋅m.
• E is the electric field strength measured in N/C.

Gauss's Law

• Gauss's Law relates the electric flux through a closed surface to the enclosed electric charge.
• Electric flux (ΦE) measures the electric field through an area and is defined as ΦE = ∫ E ⋅ dA.
• ΦE is the electric flux measured in N⋅m^2/C.
• E is the electric field strength measured in N/C.
• A is the area vector measured in m^2.
• Gauss's Law states the total electric flux through a closed surface is proportional to the enclosed electric charge: ΦE = Qenc / ε0.
• Qenc is the enclosed charge measured in C.
• ε0 is the permittivity of free space (approximately 8.854 × 10-12 C^2/N⋅m^2).
• Gauss's Law simplifies calculating electric fields for symmetric charge distributions such as spherical, cylindrical, and planar symmetries.