Electrostatics and Electric Circuits Overview

Electrons

Charges outside the atom that carries negative charges.

Protons

Charges at the center of an atom that carries positive charges.

Neutral

An atom that has equal number of protons and electrons, meaning, no overall charge.

Law of Charges

When two objects are rubbed against each other, stationary electric charge is produced.

1st Law of Charge

Opposite charges attract each other. Like charges repel each other.

2nd Law of Charge

Induction: There's no physical contact between a charged and neutral body.

Conductors

Materials that allow the electrons to pass or flow through. Best conducting material is silver.

Insulators

Materials that do not allow or hinder the electrons to pass or flow through. Best insulating material is rubber.

Electric Force (Coulomb's Law)

In the SI system of units, electric charge is measured by coulombs (C) in honor of French physicist Charles de Coulomb.

Force of Repulsion

Two charges have the same sign (positive-positive, negative-negative).

Force of Attraction

Two charges have opposite sign (positive-negative).

Law of Conservation of Charges

This law states that charge can be transferred from one object to another but cannot be created nor destroyed.

Friction

Results when two objects are rubbed against each other.

Coulomb's Law

The mathematical formula to calculate the electrostatic force between two charged particles q1 and q2 separated by a distance r.

Electric Charge

The physical property of matter that causes it to experience a force when placed in an electromagnetic field.

Charging Process

Three processes of charging: Friction, Conduction, Induction.

Potential Difference (Voltage)

The difference in electric potential between two points.

Electric Potential Energy

The energy a charged object has due to its position in an electric field.

Electric Field

A field around charged particles that exerts a force on other charged particles.

Capacitance

The ability of a system to store an electric charge.

Ohm's Law

The relationship between current, voltage, and resistance in an electrical circuit.

Circuit

A complete path through which electric charges can flow.

Series Circuit

A circuit in which the components are connected in a single path.

Parallel Circuit

A circuit in which the components are connected across common points or junctions.

Coulomb's Law

𝑭= 𝒌𝒒𝟏𝒒𝟐/𝒓𝟐

Conduction

Results when there's a physical (direct) contact between a charging and a neutral body.

Second charge

𝑞2

New 2nd charge (doubled)

𝟐𝒒𝟐

Distance

𝑟

Force

𝑭: force between charges expressed in Newtons (𝑁)

Point charges

𝒒𝟏 𝒂𝒏𝒅 𝒒𝟐: point charges expressed in coulomb (𝐶)

Distance between charges

𝒓: distance between the two charges in meter (𝑚)

Coulomb's constant

𝒌= 𝟖. 𝟗𝟖𝟖× 𝟏𝟎𝟗𝑁𝒎𝟐

Magnitude of electric force

The magnitude of the electric force 𝐹 is directly proportional to the amount of one electric charge 𝑞1 multiplied by other 𝑞2, and inversely proportional to the square of the distance 𝑟 between their centers.

New electric force (doubled charges)

If both charges are doubled to 2𝑞1 and 2𝑞2 but the distance 𝑟 remains the same, the new electric force is _____ the old force.

New electric force (distance doubled)

If both charges remain the same but the distance 𝑟 is doubled, the new electric force is _____ the old force.

Conversion of Units

1 ∁ = 1,000,000 𝝁∁

Electric force when distance is doubled

The new electric force is 1/4 times weaker than the old force.

Force of repulsion

The force of repulsion between two objects is 4.5 × 10^9 𝑁.

Distance between charges

If the charges of the objects are 2 𝐶 and 1 𝐶, determine the distance between them.

Electrical force between charges

Determine the force and the type of electrical force between two charges where one has a charge of +2 𝐶 and the other one has −1 𝐶 positioned 2 𝑚 from each other.

Magnitude of repulsive force

Calculate the magnitude of the repulsive force between two balloons with a charge of −4.0 𝜇∁ held 0.70 𝑚 apart.

First charge

1st charge (remains): 𝒒𝟏

Second charge

2nd charge (remains): 𝒒𝟐

Given values for calculation

𝑞1 = +2 ∁, 𝑞2 = +3 ∁, 𝑟= 0.5 𝑚

Force calculation

Using Coulomb's Law, compute for the unknown variables.

Electric field

IV. Electric field

Electric Field

The region where an electric force acts on charged body.

Direction of Electric Field (Positive Charge)

Away (outwards) from the charge.

Direction of Electric Field (Negative Charge)

Inwards towards the charge.

Intensity of Electric Field

Operationally defined as the ratio of the electric force 𝐹 to the charge 𝑞 placed at that point in the field.

Electric Field Formula (Force)

𝑬 = 𝑭/𝒒

Electric Field Formula (Charge)

𝑬 = 𝒌𝒒/𝒓²

Charge Formula (Electric Field)

𝒒 = 𝑬𝒓²/𝒌

Charge Formula (Force)

𝒒 = 𝑭/𝑬

Force Formula

𝑭 = 𝑬𝒒

Units of Electric Field

Expressed in Newtons per Coulomb (𝑁/𝒞).

Units of Force

Expressed in Newtons (𝑁).

Units of Charge

Expressed in Coulombs (𝐶).

Distance Between Charges

Expressed in meters (𝑚).

Coulomb's Constant

𝒌 = 8.988 × 10⁹ 𝑁𝑚²/𝐶².

Electric Potential Energy

The energy needed to move an electric charge against an electric field.

Electric Potential

Defined as the amount of electric potential energy per unit charge.

Electric Potential Energy Formula

𝑼 = 𝒒𝑬𝒓

Electric Potential Formula

𝑽 = 𝑼/𝒒

Electric Potential Energy Units

Expressed in Joules (𝑱).

Electric Potential Units

Expressed in Volts (𝑽).

Example Charge

A charge of 0.000025 ∁ is placed in an electric field whose intensity is 8.0 × 10⁶ N/∁.

Force Calculation Example

𝑭 = (8.0 × 10⁶ 𝑁/∁)(0.000025 ∁) = 200 𝑁.

Electric Potential Energy Calculation Example

For charges +3 𝜇∁ and -2 𝜇∁ positioned 1 𝑚 apart, calculate using 𝑼 = 𝒌𝒒₁𝒒₂/𝒓.

Distance Conversion Example

8 𝑐𝑚 = 0.08 𝑚.

Electric Potential (EP)

The energy stored directly onto the plates of a capacitor.

Formula for Electric Potential (V)

V = kq/r, where k = 8.988 x 10^9 N m^2/C^2 and q = 7.58 x 10^-12 C.

Current (I)

The rate of flow of charge per unit time, expressed as I = q/t.

Unit of Current

Ampere (A), named after Andre-Marie Ampere.

Resistance (R)

The electric property that impedes the flow of current.

Unit of Resistance

Ohms (Ω).

Electric Potential Difference

The difference in electric potential between the final and initial location when work is done upon a charge.

Ohm's Law

States that the current flowing through a circuit is directly proportional to the potential difference and inversely proportional to the resistance.

Capacitance

The ability of a device to store electric charge.

Dielectric

A material used to separate the conductive plates of a capacitor, allowing for smaller plate separations and higher capacitance.

Voltage (V)

The potential difference expressed in volts (V).

Current in a Circuit

The sum of the currents in each branch of a parallel circuit.

Parallel Circuit

An electric circuit with two or more components connected across two common points to allow separate conducting paths.

Series Circuit

An electric circuit with several components arranged to allow current to flow through one single path.

Total Resistance in Series

The sum of the individual resistances in a series circuit.

Total Voltage in Series

The sum of all the individual voltages in the circuit.

Total Current in Series

The same current flows through all parts of the circuit.

Total Resistance in Parallel

The reciprocal of the total resistances is equal to the sum of the reciprocals of the separate resistances.

Example of Current Calculation

What current is in an electric iron having a hot resistance of 22 Ω when across a 200 V line? I = 200 V / 22 Ω = 9.09 A.

Example of Resistance Calculation

What is the resistance of an automobile through which 2.50 A flows when 12.0 V is applied? R = 12.0 V / 2.50 A = 4.80 Ω.

Charging and Discharging Rates

Charging and discharging rates are faster than a battery.

Energy Storage in Capacitors

The potential energy is stored in the electric field.

Energy Storage in Batteries

The potential energy is stored in the form of chemical energy, which is later converted to electric energy.