Electric Charges and Fields Study Notes

The branch of Physics which deals with the effects of static electric charge is known as electrostatics or static electricity.
Emphasis is on the interaction between electric charges and the fields produced by them.

Observation of electric phenomena dates back approximately 2500 years to Thales, who noted that rubbing amber with wool allowed it to attract light materials.
This observation remained trivial for nearly 2000 years until Gilbert discovered that various materials, including glass and ebonite, could acquire electric charge through friction.
A material becomes "electrified" through this process, and the resulting property is termed "frictional electricity."
Electric charge is defined as the property acquired by a material when it becomes electrified.

Examples of Electrification:
- Glass Rod and Silk: Glass rubbed with silk acquires a positive charge.
- Ebonite Rod and Cat-Skin: Ebonite rubbed with cat-skin acquires a negative charge.
When the two similar materials are brought close, they repel each other; when opposites are brought close, they attract.
- Benjamin Franklin’s classification:
- Positive charge: developed on a glass rod rubbed with silk.
- Negative charge: developed on an ebonite rod rubbed with cat-skin.
Key findings:
- Like charges repel each other while unlike charges attract each other.

Charge Cancellation: Positive and negative charges combine to cancel each other's effects (similar to positive and negative numbers in mathematics).
Attraction vs. Repulsion: Attraction does not imply opposite charge; uncharged objects can also be attracted due to induction. However, repulsion confirms that an object is charged.
Electroscopes: Instruments used to detect charge type and amount, with the gold leaf electroscope as a common example.

Based on the atomic model, each atom contains positively charged protons and neutrally charged neutrons in a nucleus, surrounded by negatively charged electrons.
An atom remains neutral when the number of electrons equals protons, meaning no net charge.
Electrification occurs when:
- Electrons are lost: The atom becomes positively charged (deficiency of electrons).
- Electrons are gained: The atom becomes negatively charged (excess of electrons).
The modern understanding emphasizes that only electrons are involved in charge transfer, not protons.

Electron Transfer: Occurs only when different materials are rubbed together; electron transfer involves mass exchange.
Charge Series: The materials tend to lose or gain electrons following an established series (e.g., cat-skin loses electrons, glass gains).

Conductors: Materials that allow electric charge to flow, e.g., metals, human body, earth, mercury, electrolytes.
Insulators: Materials that do not allow electric charge to flow, e.g., glass, rubber, plastic.
Charge distribution varies in conductors (spreads across surface) vs. insulators (stays localized).

Conduction: Occurs when a charged object makes contact with an uncharged conductor, transferring charge.
Induction: A method to induce charge in an uncharged conductor without contact, whereby charge redistributes internally as electrons are attracted/repelled by a nearby charged object.
After the charged object is removed, the induced charge remains localized.

Coulomb (C): The unit of electric charge defined by flow through a conductor carrying 1 ampere for 1 second:
$1 ext{ C} = 1 ext{ A} imes 1 ext{ s}$ .
Fundamental charge of an electron: $1.6 imes 10^{-19} ext{ C}$ .

Quantization of Electric Charge: Electric charges are quantized, always found in integral multiples of the smallest amount of charge (elementary charge, denoted by $e$ ).
- Charge expressions: $q = ±ne$ (where $n$ is an integer).
Conservation of Electric Charge: Charge cannot be created or destroyed. The total charge in a closed system remains constant, validated through multiple experiments.
- Samples of transfer support this principle:
  - Rubbing rods where charge appears equivalently on both objects.
Invariance Property: The amount of charge remains constant irrespective of motion.

Describes the interaction between charges, stating that:
$F ext{ (force)} ext{ is directly proportional to the product of the charges and inversely proportional to the square of the distance between them:}$
$F = k rac{q<em>1 q</em>2}{r^2}$
Constants include:
- Proportionality constant $k$ varies based on medium properties, with a common vacuum value of $k = 9.0 imes 10^9 ext{ N m}^2/ ext{C}^2$ .
Comparison of electrical force to gravitational force highlights key differences:
- Electric forces can be attractive and repulsive, gravity is always attractive.
- Electric forces are stronger than gravitational forces typically by factors ranging from $10^{36}$ to $10^{43}$ .

Explains the dynamics in cases where charges vary based on distance and direction using vector analysis,
- Forces are equal and opposite, consistent with Newton's third law.

For multiple charges in proximity, the net force on any charge equals the vector sum of all forces exerted by others:
$ext{F}<em>1 = ext{F}</em>{12} + ext{F}_{13} + …$

A charged body reaches equilibrium under conditions where the net electric force acting on it is zero.

Defined by the force experienced by a test charge placed within the field by a source charge:
$E = rac{F}{q}$
The electric field is a conservative force field.
Distinction between intensity due to individual point charges and continuous distributions.

Determined by the application of Coulomb’s law, evaluating the force on a test charge at a given distance.
Superposition applies for systems with more than one point charge

Describes linear, surface, and volume charge distributions; each analyzed by integrating elementarily across their respective extents.

Visualization of electric fields characterized by direction (towards negative charges, away from positive charges) and density reflecting electric field strength.
Properties include originating on positives and terminating on negatives, no intersections possible, and presence in non-conductive regions only.
Electric dipoles, defined by their respective charge arrangements, lead us to the dipole moment and its relation to electric field.

An electric dipole experiences a torque (but no net force) in a uniform field, aligning itself toward the field direction. The torque $au$ is defined as:
$au = pE ext{ sin} heta$