7.5 Equipotential Surfaces and Conductors
3 min read•june 24, 2024
and are key concepts in understanding electric fields. They help visualize how electric charges interact and how energy is distributed in space. These ideas are crucial for grasping the behavior of electric fields and their effects on charged particles.
Conductors play a unique role in electrostatics, with special properties at equilibrium. Understanding how charges distribute on conductors and their effects on nearby electric fields is essential for many practical applications, from lightning rods to electronic devices.
Electric Potential and Equipotential Surfaces
Equipotential surfaces and field lines
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- Equipotential surfaces are surfaces where all points have the same
- Work done by an electric field to move a charge between any two points on an is zero (moving a charge from one side of a metal sphere to the other)
- are always perpendicular to equipotential surfaces
- No work is done when moving a charge along an equipotential surface (moving a charge along the surface of a metal plate)
- The electric field is strongest where equipotential surfaces are closest together
- Closely spaced equipotential surfaces indicate a strong electric field (near a )
- Widely spaced equipotential surfaces indicate a weak electric field (far from a point charge)
- The concept of is closely related to equipotential surfaces and field lines
Mapping of equipotential lines
- for a point charge are concentric circles centered at the charge
- Spacing between lines decreases as distance from the charge decreases, indicating a stronger field closer to the charge (lines are closer near the charge)
- Equipotential lines for a are evenly spaced parallel lines
- Field strength is constant, so spacing between lines is constant (between two large parallel plates)
- Equipotential lines for an form closed loops around the charges
- Lines are closest together near the charges, indicating a stronger field in those regions (near the positive and negative ends of a dipole)
Conductors and Electric Fields
Conductors at electrical equilibrium
- Electric field inside a at equilibrium is zero
- Any resides on the surface of the (charge on a metal sphere's surface)
- Electric potential is constant throughout a conductor at equilibrium
- Conductor can be considered an equipotential surface (a metal box forms an equipotential surface)
- Net charge inside a conductor is zero at equilibrium
- Positive and negative charges redistribute until the electric field inside is zero (electrons move to cancel out field)
- This principle is the basis for
Charges near conductor surfaces
- Excess charge on a conductor resides entirely on its surface
- depends on the shape of the conductor and external electric fields (more charge at sharp points)
- Electric field just outside a charged conductor is perpendicular to its surface
- Field lines originate or terminate perpendicular to the surface (field lines leave a positively charged sphere radially)
- Electric field strength is greatest where the surface curvature is highest
- is highest at sharp points or edges (charge concentrates at the tip of a )
- The shape and size of a conductor affect its
Equipotential lines vs topographic contours
- Equipotential lines in electrostatics are analogous to elevation contours in topography
- Points on the same contour line have the same elevation (points at 100 m elevation on a topographic map)
- Points on the same have the same electric potential (10 V equipotential surface around a charge)
- Electric field lines are analogous to the steepest path down a hill
- Path of steepest descent is always perpendicular to elevation contours (water flows perpendicular to contour lines)
- Electric field lines are always perpendicular to equipotential surfaces (field lines cross equipotentials at 90°)
- Spacing between contour lines indicates the steepness of the terrain
- Closely spaced contours indicate a steep slope (contours bunched together on a cliff face)
- Closely spaced equipotential lines indicate a strong electric field (dense equipotentials near a point charge)
Gauss's Law and Applications
- relates electric flux through a closed surface to the enclosed charge
- It provides a powerful method for calculating electric fields in symmetric situations
- The is an application of Gauss's law and electrostatic shielding
Key Terms to Review (26)
Capacitance: Capacitance is the ability of a system to store charge per unit voltage. It is measured in farads (F).
Capacitance: Capacitance is a measure of the ability of a capacitor to store electric charge. It is a fundamental quantity in the study of electricity and electronics, and it plays a crucial role in various topics related to electrostatic equilibrium, electric potential, and energy storage.
Charge Density: Charge density is a measure of the amount of electric charge per unit volume or unit area in a given system. It is a fundamental concept in electrostatics that describes the distribution and concentration of electric charges within a material or space.
Charge Distribution: Charge distribution refers to the spatial arrangement and density of electric charges within a system or object. It is a fundamental concept in electrostatics that describes how electric charges are distributed and how this distribution influences the resulting electric fields and potentials.
Conductor: A conductor is a material that allows the free flow of electric charge, typically electrons. Metals like copper and aluminum are common examples of conductors.
Conductor: A conductor is a material that allows the free flow of electric charge, enabling the efficient transfer of electrical current. This property is crucial in various topics within physics, including conductors, insulators, and charging by induction, as well as in understanding equipotential surfaces, Ohm's Law, and motional electromotive force (EMF).
Continuous charge distribution: A continuous charge distribution is a model where the electric charge is spread over a region of space rather than being confined to discrete points. This concept is used to calculate the electric field produced by objects with uniformly distributed charges.
Electric dipole: An electric dipole consists of two equal and opposite charges separated by a small distance. It creates an electric field and has a dipole moment, which is a vector quantity pointing from the negative to the positive charge.
Electric Dipole: An electric dipole is a pair of equal and opposite electric charges separated by a small distance. It is a fundamental concept in electrostatics that describes the electric field and potential created by a pair of equal but opposite charges.
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.
Electrical Equilibrium: Electrical equilibrium refers to a state in which the net electric force acting on charges within a system is zero, meaning there is no further movement of charge. In this state, the electric field inside a conductor is also zero, leading to stable distributions of charge on conductors and equipotential surfaces. This balance ensures that charges remain uniformly distributed, preventing any potential differences that could cause current flow.
Electrostatic Shielding: Electrostatic shielding is the process of blocking or containing electric fields within a specific region by using a conductive material or surface. It is a fundamental concept in the study of conductors, electrostatic equilibrium, and equipotential surfaces.
Equipotential line: An equipotential line is a line or curve in a field where the electric potential is constant. No work is required to move a charge along an equipotential line.
Equipotential Lines: Equipotential lines are imaginary lines in an electric field that connect points with the same electric potential. These lines represent the spatial distribution of electric potential and provide a visual representation of the electric field.
Equipotential surface: An equipotential surface is a surface on which every point has the same electric potential. This implies that no work is required to move a charge anywhere along this surface.
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.
Excess Charge: Excess charge refers to the unequal distribution of electric charges within a conductor or on the surface of a conductor. This imbalance of charges creates an electric field and potential difference, which are important concepts in the study of electrostatics and the behavior of conductors.
Faraday Cage: A Faraday cage is an enclosure formed by conducting material that blocks external static and non-static electric fields by channeling the electric charges to the exterior of the enclosure. It is named after the English scientist Michael Faraday, who discovered the principle in 1836.
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.
Lightning rod: A lightning rod is a metal rod mounted on a structure to protect it from lightning strikes by directing the electrical discharge safely into the ground. It acts as a conductor, providing a low-resistance path for the electric current.
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.
Topographic Contours: Topographic contours are lines on a map that connect points of equal elevation, representing the shape and relief of the land. They are an essential tool for visualizing and understanding the three-dimensional terrain in the context of equipotential surfaces and conductors.
Uniform Electric Field: A uniform electric field is a region of space where the electric field is constant in both magnitude and direction. This means the electric field lines are parallel and evenly spaced, creating a uniform force on any charged particles within the field.