Study Notes: Electric Charges and Forces (Ch. 22)

Electric Charges and Forces

Concept: Electric Charge

Electric charge is a fundamental property of matter, similar to mass. Atoms are composed of protons, neutrons, and electrons, with protons and electrons carrying electric charge.

• Electric Charge (q): A property that causes matter to experience a force when placed in an electric or magnetic field.

• Elementary Charge (e): The magnitude of the charge of a single proton (positive) or electron (negative): $e = 1.602 \times 10^{-19}~\text{C}$

• Protons: Charge $= +e$

• Electrons: Charge $= -e$

• Neutrons: Charge $= 0$

Mass (kg)	Electric Charge (C)
Mass → Gravitational Force	Electric Charge → Electric Force
Mass always positive	Charge can be positive or negative

• Net charge of an atom: $q = (+e \times \text{number of protons}) + (-e \times \text{number of electrons})$

• Most materials are electrically neutral (equal numbers of protons and electrons).

Practice: Charge of Atom

• To find the charge of an atom, subtract the number of electrons from the number of protons and multiply by $e$.

• Example: An atom with 16 protons and 17 electrons has a net charge of $q = (16 - 17) \times e = -e$.

Example: Number of Electrons

• To find the number of electrons corresponding to a charge $q$, use $n = \frac{|q|}{e}$.

• Example: $1.5 \times 10^{-7}~\text{C}$ corresponds to $n = \frac{1.5 \times 10^{-7}}{1.602 \times 10^{-19}} \approx 9.4 \times 10^{11}$ electrons.

Example: Electrons in Water

• Given water's density and molecular weight, calculate the number of molecules and thus electrons in a given volume.

• Example: 20 L of water, with 10 electrons per molecule, calculate total electrons and total charge.

Concept: Charging Objects

Objects can be charged by transferring electrons, resulting in a net electric charge.

• Conductors: Allow electrons to move freely (e.g., metals).

• Insulators: Do not allow electrons to move freely (e.g., plastic, rubber).

• Rubbing: Transfers electrons from one object to another (e.g., rubbing plastic rod with fur).

• Like charges repel, unlike charges attract.

Polarization

• Separation of charges within an object without net charge transfer.

• Occurs in both conductors and insulators.

Conduction vs. Induction

• Conduction: Transfer of charge by direct contact; results in net charge transfer.

• Induction: Charging without direct contact; involves rearrangement of charges and grounding.

Steps for Charging by Induction

1. Connect neutral conductor to ground.

2. Bring charged rod near conductor (without touching).

3. Remove ground connection, then remove rod.

4. Conductor is left with net charge opposite to that of the rod.

Concept: Conservation of Charge

Electric charge is conserved; it cannot be created or destroyed, only transferred.

• When objects interact, the total charge before and after remains the same.

• Charge can only be moved from one object to another.

Example: Sharing Charge

• When two conductors touch, charge redistributes until equilibrium is reached.

• Example: If a $-1~\text{C}$ and $+3~\text{C}$ sphere touch, total charge is $+2~\text{C}$, so each ends with $+1~\text{C}$ if identical.

Concept: Coulomb's Law

Coulomb's Law quantifies the electric force between two point charges.

• The force between two charges $q_1$ and $q_2$ separated by distance $r$ is:

$F = k_e \frac{|q_1 q_2|}{r^2}$

• $k_e = 8.99 \times 10^9~\text{N} \cdot \text{m}^2/\text{C}^2$ (Coulomb's constant)

• Force is attractive for unlike charges, repulsive for like charges.

Comparison: Electric vs. Gravitational Force

• Electric forces are much stronger than gravitational forces for elementary particles.

Practice and Examples

• Changing Distance: If the distance between charges increases, the force decreases by the square of the distance.

• Charges in a Line: Calculate net force on a charge due to other charges using vector addition.

• Charges in a Plane: Use vector components to find net force when charges are arranged in two dimensions.

• Symmetry: Exploit symmetry to simplify force calculations (e.g., equal charges at equal distances).

Sample Problems

• Find the net force on a charge at the center of a square with charges at the corners.

• Calculate the charge on leaves of an electroscope given their separation and mass.

Summary Table: Key Properties of Electric Charge

Property	Description
Quantization	Charge exists in integer multiples of $e$
Conservation	Total charge is constant in an isolated system
Attraction/Repulsion	Like charges repel, unlike charges attract
Unit	Coulomb (C)

Additional info: These notes expand on the provided study prep by including definitions, formulas, and academic context for each concept, as well as worked examples and summary tables for clarity.