Electric Charge and Electric Fields – Physics for Life Sciences II (Lecture 6)

Electric Charge

Definition and Properties of Electric Charge

Electric charge is a fundamental property of matter that enables it to experience forces of attraction or repulsion. Charged objects can interact with each other through these forces, which are the basis of many physical phenomena.

• Electric Charge: A property of matter that causes it to experience a force when placed in an electromagnetic field.

• Types of Charge: There are two types of electric charge: positive and negative.

• Interaction: Like charges repel each other, while opposite charges attract.

• SI Unit: The standard unit of electric charge is the Coulomb (C).

• Elementary Charge: The smallest unit of charge is the elementary charge, $e = 1.602 \times 10^{-19}$ C.

Example: Rubbing a glass rod with silk transfers electrons, charging the rod and silk with opposite charges. Two charged rods repel, while a charged rod and silk attract.

Quantization and Conservation of Charge

Electric charge is quantized and conserved in all physical processes.

• Quantization: Charge exists in discrete packets, always as integer multiples of the elementary charge $e$.

• Conservation: Charge can be transferred between objects but cannot be created or destroyed.

Example: In atoms, the number of protons (positive charge) equals the number of electrons (negative charge), resulting in a neutral atom.

Conductors and Insulators

Movement of Charge

Materials are classified based on their ability to allow electric charge to move.

• Conductors: Materials (e.g., metals, salty water) where charges can move freely. Electrons are not bound to individual atoms.

• Insulators: Materials (e.g., pure water, plastic) where electrons are tightly bound and cannot move freely.

• Charging by Contact: Neutral objects can be charged by transferring electrons through friction or contact.

• Charging by Induction: Objects can be charged without direct contact by rearranging charges using a nearby charged object.

Example: Rubbing a balloon on hair transfers electrons, charging both objects.

Polarization and Electric Dipoles

Polarization of Molecules

Some molecules can be polarized, meaning their positive and negative charges are separated within the molecule.

• Polar Molecules: Molecules like water have a permanent electric dipole moment.

• Electric Dipole: A pair of equal and opposite charges separated by a distance $d$.

Example: Water molecules are polar and can align in an electric field.

Coulomb's Law

Force Between Point Charges

Coulomb's Law describes the magnitude and direction of the force between two point charges.

• Formula:

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

• Direction: The force is along the line joining the charges. Like charges repel, opposite charges attract.

• Vector Form:

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

• Superposition Principle: The net force on a charge due to multiple other charges is the vector sum of the individual forces.

Example: Calculating the net force on a charge placed between two other charges along a line.

Vectors and Vector Addition

Vector Representation and Addition

Forces and fields are vector quantities, having both magnitude and direction.

• Vector Addition: Vectors are added using the head-to-tail method or by components.

• Components: Any vector $\vec{A}$ can be written as $A_x$ and $A_y$ using trigonometry:

$A_x = A \cos \theta$ $A_y = A \sin \theta$

• Magnitude and Direction: The magnitude of the resultant vector $\vec{C}$ is found using the Pythagorean theorem:

$|\vec{C}| = \sqrt{C_x^2 + C_y^2}$

• Direction: $\tan \phi = \frac{C_y}{C_x}$

Example: Adding two force vectors acting at an angle to find the net force.

Electric Field

Definition and Properties

The electric field is a vector field that describes the force experienced by a test charge at every point in space.

• Electric Field ($\vec{E}$): Defined as the force per unit charge:

$\vec{E} = \frac{\vec{F}}{q}$

• Source Charges: The charges that create the electric field.

• Test Charge: A small positive charge used to probe the field without affecting it.

• Direction: The field points away from positive charges and toward negative charges.

Example: Placing a test charge near a group of source charges to determine the direction and magnitude of the field.

Electric Field Lines

Visualizing Electric Fields

Electric field lines are used to represent the strength and direction of the electric field in space.

• Properties of Field Lines:

  • Field lines begin on positive charges and end on negative charges or at infinity.

  • Field lines never cross.

  • The density of field lines indicates the strength of the field (closer lines = stronger field).

  • Field lines are perpendicular to the surface of conductors.

• Uniform vs. Non-uniform Fields: In a uniform field, the spacing between lines is constant; in a non-uniform field, spacing varies.

Example: The pattern of field lines around a single point charge or between two opposite charges (dipole).

Summary Table: Properties of Conductors and Insulators

Material Type	Charge Movement	Examples
Conductor	Charges move freely	Metals, salty water
Insulator	Charges are tightly bound	Plastic, pure water

Key Equations

• Coulomb's Law: $F = k_e \frac{|q_1 q_2|}{r^2}$

• Electric Field: $\vec{E} = \frac{\vec{F}}{q}$

• Vector Components: $A_x = A \cos \theta$, $A_y = A \sin \theta$

• Resultant Vector Magnitude: $|\vec{C}| = \sqrt{C_x^2 + C_y^2}$

Additional info: Some context and examples were inferred from standard introductory physics curriculum to clarify fragmented points and ensure completeness.