Electric Charge and Charging Methods

• Electric charge comes in two types: positive (protons) and negative (electrons), each with an absolute value of 1.6 X 10-19 Coulombs.
• Like charges repel, while opposite charges attract.
• The law of conservation of charge states that charge cannot be created or destroyed, only transferred.
• Proton mass is 1.673 X 10-27 kg, neutron mass is 1.673 X 10-27 kg, and electron mass is 9.109 X 10-31 kg.
• Charges of the electron and proton are equal in magnitude.
• Conductors allow free movement of charges, while insulators do not. Metals are generally good conductors, and nonmetals are insulators. Semiconductors have intermediate properties.

Methods of Charging

• Friction involves rubbing objects together to transfer charge.
• Conduction allows charge transfer through direct contact.
• Induction redistributes charge in a neutral object when a charged object is brought nearby.

Charging by Induction

• Charging occurs when a charged object near a neutral one causes charge redistribution without contact.
• The neutral object then develops regions of opposite charges.
• Grounding the neutral object allows it to permanently acquire a charge opposite to that of the inducing object.
• Steps: Bring a charged object near, rearrange free electrons, ground the conductor (electrons flow in/out causing net charge), remove ground, and remove the inducing object, the conductor retains opposite charge.

Coulomb's Law

• The electric force between two charged objects is proportional to the product of the charges.
• The force is inversely proportional to the square of the separation distance between the objects. The equation is F = k (q1q2 / r² ).
• F is the electrostatic force.
• q1 and q2 are the charges.
• r is the separation distance
• k = 8.988 x 10^9 N m²/C², which is the proportionality constant.

Electric Force

• The electric force is a vector quantity.
• Coulomb's Law is rewritten as F12 = k (q1q2 / r² ) r^12, where r^12 is a unit vector pointing from object 1 to object 2.
• The force's direction is either parallel or antiparallel to this unit vector, which depends upon the relative signs of the charges.
• The force acting on each charged object has the same magnitude but acts in opposite directions.

Coulomb's Law - Electric Force

• The magnitude of electric force between two-point charges is directly proportional to the product of their charges.
• It is also inversely proportional to the square of the distance between them.

Superposition of Forces

• The net force on any one of the charged objects is the vector sum of the individual Coulomb forces on that charged object.
• The electric force can be thought of as being mediated by an electric field.
• A field can be a scalar field (magnitude only, e.g., temperature) or a vector field (magnitude and direction, e.g., electric field).

Electric Field (E)

• A charged object placed at a point in space creates an electric field throughout the surrounding space.
• This field exerts a force on another charged object.
• The electric field is also a vector.
• If an electric force acts on an object with charge q0, the electric field at that point is given by E = F / q0.
• Force on a positively charged object is in the same direction as the electric field, while force on a negative charge is opposite.
• A positive charge sets up an electric field pointing away, and a negative charge sets up an electric field pointing toward it.

Electric Field Lines

• An imaginary line tangent to the direction of the electric field at that point.
• The spacing or density of lines relates to the electric field magnitude.
• Electric field has unique direction at any given point.
• Lines begin on positive charges and end on negative charges.
• Electric field of a point charge: E = k (q / r²) r^
• For multiple charged objects, the net electric field is the vector sum of individual electric fields.

Electric Dipole

• An electric dipole consists of a pair of point charges that have equal magnitude but opposite signs separated by a distance d.
• Torque on a Dipole equation: t = q(dxE)

Electric Potential Energy (U) and Electric Potential (V)

• The total energy of the particle remains constant: KEa + PEa = KEb + PEb
• Wa→b = -(Ub - Ua) = −ΔU
• Ub Up-Ua = ∫F · ds = -qEuniform (Yb – Ya)
• Potential Energy (U) increases if the particle moves in the direction opposite to the force on it requiring work or by an external agent
• Potential Energy (U) decreases if the particle moves in the same direction as the force on it

Electric Potential

• Like energy, potential is a scalar.
• Electric potential is defined by Potential = V = (1 / 4πεor) (q / r).
• This has the convention that potential is zero at infinite distance
• The units of electric potential are Volts which is the definition of Energy / Charge.
• Potential (V) increases if you move in the direction opposite to the electric field, and it decreases if you’re in the same direction as the electric field.

Work and Potential equation

• Work done by the electric force equation: Vb-Va=-∫E*dl

Capacitance

• Device stores electrical energy and releases it.

Capacitors

• Two conductors carry charges q and -q; separated by an insulator
• Capacitors cannot create charge; it accumulates and holds charge temporarily.
• Capacitors remain neutral overall, but store charge Q.
• Charge amount depends on applied Voltage and Capacitor's size.

Charging/Storing Energy in a Capacitor

• Conductors initially have zero net charge.
• When conductors are connected, electrons gets transferred from one conductor to the other.
• After, one conductor has net positive charge, other has net negative charge, but the capacitor remains ZERO.

Capacitance

• Ratio of the magnitude of the charge over potential difference: C = Q / Vab. C is Capacitance. Q is Charge Magnitude in Coulombs. Vab potential difference.
• Units: 1 Farad = 1 Coulomb/1 Volt
• Capacitance (↑), Charge (↑), Energy (↑)
• Capacitance (↓), Charge (↓), Energy (↓)

Capacitors in Vacuum

• Conductors on the capacitors are separated by a vacuum
• Parallel-plate Capacitors has parallel conducting plates with area A (separated by distance d).
• The magnitude of the electric field equation: E = σσ/Εο E= magnitude of Electric Field. σ = Surface charge density ६०= permittivity of free space Q = charge in coulomb A = area of the plate

Equation for Capacitance

• Equation for Capacitance of a parallel plate: C = Εο * A / d

Capacitors in Series

• Series occurs where charge travels one way form a point to point
• Magnitude of charge Q on plates is the same
• To get potential differences: Vac + Vcb Vab
• The equivalent capacitance Ceq equation: Vab = V1 + V2 = (Q/C1) + (Q/C2)
• Equivalent capacitance must have less than the individual capacitance in dividual capacitance
• 1/ Ceq = 1/C1 + 1/C2 + 1/C3+1/Cn

Capacitors in Parallel

• Connection travels in two or more paths from point a to point b
• Potential difference for all capacitors is the same and equal to Vab
• Charge stored equation: Q = (C₁ + C2)Vab

Dielectrics

• Are solid, non-conductive that gets inserted into parallel plates that’s non vacuum
• Keep two larger metal sheets apart at very small distances without touching
• Tolerate stronger electric fields without electric breakdown compared to air
• Capacitance is higher when dielectric material is placed
• Dielectric constant V/K
• Capacitance and potential difference: C = KCO (Dielectric in capacitance), V = Vo/ K (Potential of Dielectric)

Polarization

• The process where the positive charges in a material shift due to electric field.
• Permittivity of dielectric material: E = KEO

Capacitance General Equations

• In Vacuum equations: E/d (Capacitance). EO QdA / ErA1 or Eo 4 (Potential difference) = 212 2V (Energy stored) /2A (Energy density

Capacitance With Dielectric

A (Capacitance) 12 (Energy stored)

Electric Current

• Motion of any charge from another to the other
• Current is electric charges that passes time.
• Steady current in a conductor requires electric field inside
• Electrons drift to the opposite Equation dQ (Coulomb (A) + sec