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Electric fields are the invisible forces that surround electric charges. They're like invisible rubber bands, stretching out from positive charges and pulling towards negative ones. Understanding electric fields helps us grasp how charges interact without touching.

Visualizing electric fields is key to grasping their behavior. Field lines show the direction and strength of the field, with more lines meaning a stronger field. Calculating field strength helps us predict how charges will move and interact in different situations.

Electric Field

Electric field definition and role

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  • (E⃗\vec{E}) is a that exists in the space surrounding an electric charge or a collection of charges
    • Represents the force per unit charge that would be experienced by a positive placed at any point in the field
    • Mathematically expressed as E⃗=F⃗q\vec{E} = \frac{\vec{F}}{q}, where F⃗\vec{F} is the force on a test charge qq
  • Electric field allows for the description of electric forces without considering the test charge
    • Depends only on the source charge(s) creating the field, not the test charge
    • Enables the determination of the force on any charge placed in the field by multiplying the field strength by the charge value

Visualization of electric field lines

  • are a visual representation of the electric field
    • Direction of the field line at any point indicates the direction of the force on a positive test charge (positive to negative)
    • Density of field lines represents the strength of the electric field
      • Closer field lines indicate a stronger field (near charges)
  • Field lines originate from positive charges and terminate on negative charges
    • For a single positive , field lines radiate outward uniformly in all directions (spherical symmetry)
    • For a single negative point charge, field lines converge uniformly from all directions (spherical symmetry)
  • Field lines between two opposite charges () start from the positive charge and end on the negative charge
    • Field lines are denser near the charges, indicating a stronger field (inverse square relationship)
  • Field lines between two like charges (same sign) diverge from each other
    • Field lines are denser between the charges, indicating a stronger field in that region (repulsion)
  • are perpendicular to electric field lines, representing points of equal

Calculation of electric field strength

  • describes the electric force between two point charges
    • F⃗=kq1q2r2r^\vec{F} = k \frac{q_1 q_2}{r^2} \hat{r}, where k=8.99×109N⋅m2C2k = 8.99 \times 10^9 \frac{N \cdot m^2}{C^2} (), q1q_1 and q2q_2 are the magnitudes of the charges, rr is the distance between the charges, and r^\hat{r} is the unit vector pointing from q1q_1 to q2q_2
  • Electric field due to a point charge can be derived from Coulomb's law
    • E⃗=kqr2r^\vec{E} = k \frac{q}{r^2} \hat{r}, where qq is the magnitude of the source charge, rr is the distance from the charge, and r^\hat{r} is the unit vector pointing away from the charge
    • Example: Electric field strength at 1 m from a 1 C charge is 8.99×109NC8.99 \times 10^9 \frac{N}{C}
  • For multiple point charges, the electric field at a point is the vector sum of the fields due to each individual charge ()
    • E⃗total=E⃗1+E⃗2+…+E⃗n\vec{E}_{total} = \vec{E}_1 + \vec{E}_2 + \ldots + \vec{E}_n, where E⃗i\vec{E}_i is the electric field due to the ii-th charge
    • Example: Two positive charges of 1 C each, separated by 1 m, will have a net electric field of zero at the midpoint between them
  • For continuous charge distributions (lines, surfaces, or volumes), the electric field is calculated using integration
    1. Divide the charge distribution into infinitesimal elements
    2. Calculate the field due to each element using the point charge formula
    3. Sum (integrate) the contributions from all elements to find the total field
    • Example: Electric field strength at the center of a uniformly charged ring is zero due to symmetry

Electric Flux and Gauss's Law

  • is a measure of the electric field passing through a given surface
  • relates the electric flux through a closed surface to the enclosed charge
  • The of the medium affects the strength of the electric field and is a factor in Gauss's law
  • is related to the work done by the electric field and can be used to calculate the electric field

Key Terms to Review (21)

Charles-Augustin de Coulomb: Charles-Augustin de Coulomb was an 18th century French physicist who is best known for his pioneering work in the field of electrostatics. His research and discoveries laid the foundation for our understanding of the fundamental laws governing electric charges and the forces they exert on one another.
Coulomb's Constant: Coulomb's constant, also known as the electrostatic constant or the electric force constant, is a fundamental physical constant that describes the strength of the electrostatic force between two point charges. It is a crucial parameter in understanding and quantifying various electrical phenomena, including Coulomb's law, electric fields, electric flux, electric potential energy, and applications of electrostatics.
Coulomb's law: Coulomb's law describes the force between two charged objects, stating that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This principle is crucial for understanding interactions between electric charges, influencing how charges behave in different materials, and shaping the concept of electric fields.
Dipole: A dipole is a pair of equal and opposite electric charges, typically a positive charge and a negative charge, that are separated by a small distance. This separation of charges creates an electric field and a potential difference between the two charges.
Electric field: An electric field is a vector field that surrounds electric charges and exerts force on other charges within the field. It is defined as the force per unit charge and is measured in Newtons per Coulomb (N/C).
Electric Field Lines: Electric field lines are imaginary lines that represent the direction and strength of an electric field. They are used to visualize the electric field around charged objects or between charged surfaces, providing a way to understand the forces acting on charged particles within the field.
Electric Flux: Electric flux is a measure of the total electric field passing through a given surface. It represents the number of electric field lines passing perpendicularly through a surface, and is a key concept in understanding the behavior of electric fields and charges.
Electric potential: Electric potential is the amount of electric potential energy per unit charge at a specific point in an electric field. It is measured in volts (V).
Electric Potential: Electric potential, also known as electrostatic potential, is a scalar quantity that represents the amount of work done per unit charge in moving a test charge from an infinite distance to a specific point in an electric field. It is a measure of the potential energy per unit charge at a given location within an electric field.
Electrostatic Induction: Electrostatic induction is the process by which an electrically charged object can create an opposite charge on a nearby neutral object without making physical contact. This phenomenon arises due to the rearrangement of charges within the neutral object in response to the presence of the charged object, leading to the creation of induced charges.
Equipotential surfaces: Equipotential surfaces are hypothetical surfaces where the electric potential is constant throughout. This means that any point on a given equipotential surface has the same electric potential energy per unit charge, which implies that no work is done when moving a charge along this surface. Understanding equipotential surfaces helps clarify how electric fields interact with charged objects and their distributions.
Gauss's Law: Gauss's law is a fundamental principle in electromagnetism that relates the electric flux through a closed surface to the total electric charge enclosed within that surface. It provides a powerful tool for calculating the electric field produced by various charge distributions.
Newton per Coulomb: Newton per coulomb (N/C) is a unit that measures the strength of an electric field, which is the force exerted per unit charge on a stationary test charge placed in that field. It represents the amount of force, measured in newtons, that would be exerted on a charge of one coulomb placed in the electric field.
Permittivity: Permittivity is a physical constant that describes how an electric field affects, and is affected by, a dielectric medium. It plays a crucial role in determining the strength and behavior of electric fields, influencing both the force between charges and the energy stored in capacitors. The value of permittivity varies depending on the material, affecting how electric fields interact with matter and is central to understanding capacitors and electromagnetic waves.
Point Charge: A point charge is an idealized model of an electric charge that is concentrated at a single point in space, with no physical size or dimensions. This concept simplifies the analysis of electric fields and forces, allowing for easier calculations and a clearer understanding of how electric charges interact with one another and produce electric fields.
Scalar field: A scalar field is a function that assigns a single scalar value to every point in space. In physics, it often represents quantities like temperature or electric potential that have magnitude but no direction.
Superposition: Superposition is the principle stating that the net electric field caused by multiple charges is the vector sum of the individual fields created by each charge. This allows for complex fields to be analyzed as simpler, individual contributions.
Superposition Principle: The superposition principle states that the net effect of multiple sources or influences acting on a system is the sum of their individual effects. This principle is fundamental in understanding various physical phenomena, particularly in the fields of electricity, magnetism, and wave mechanics.
Test Charge: A test charge is a small, imaginary point charge used to map and analyze the electric field around a charged object. It serves as a tool to understand the properties and behavior of electric fields without significantly disturbing the field itself.
Vector field: A vector field is a map that assigns a vector to every point in space. In the context of electric fields, it represents the direction and magnitude of the electric force experienced by a positive test charge at each point.
Vector Field: A vector field is a function that assigns a vector to every point in a specified region of space. It is a mathematical construct that describes the magnitude and direction of a quantity, such as a force or a velocity, at every point in a given space.
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Glossary
Glossary
5.5 Calculating Electric Fields of Charge Distributions