Glossary

19.2 Electric Potential in a Uniform Electric Field

2 min read•june 18, 2024

in a uniform field is all about the relationship between and electric field strength. The key equation is V = Ed, where V is voltage, E is field strength, and d is distance between points in the field.

This concept helps us understand how voltage changes with distance in a uniform field. We can use it to calculate voltage, field strength, or distance when given the other two variables. It's crucial for analyzing parallel plate capacitors and other uniform field setups.

Electric Potential in a Uniform Electric Field

Voltage and electric field relationship

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  • Voltage or directly proportional to electric field strength in uniform field
    • Relationship given by equation: V=EdV = Ed
      • VV voltage or difference
      • EE electric field strength
      • dd distance between two points in field
  • Electric field constant in magnitude and direction throughout uniform field
  • As distance between two points increases, voltage between them increases linearly, given constant electric field strength ()

Expressions for potential and field

  • Electric potential difference (voltage) in uniform field:
    • V=EdV = Ed
      • Derived from done by electric field on test charge moved between two points
      • Work done equal to change in : W=qEd=q(Vf−Vi)W = qEd = q(V_f - V_i)
      • Rearranging equation yields: Vf−Vi=EdV_f - V_i = Ed, where Vf−ViV_f - V_i voltage
  • Electric field strength in uniform field:
    • E=VdE = \frac{V}{d}
      • Obtained by rearranging equation V=EdV = Ed
      • Electric field strength voltage divided by distance between two points ()

Energy and work in electric fields

  • Potential energy in an electric field is related to the work done by the field
  • Work done by the electric field is equal to the negative change in potential energy
  • applies to charges moving in electric fields
  • are perpendicular to
  • Electric dipoles experience torque in uniform electric fields due to potential energy differences

Calculations in uniform fields

  • Use equation V=EdV = Ed to solve problems involving any two of three variables
    1. If given voltage and distance, calculate electric field strength: E=VdE = \frac{V}{d}
    2. If given electric field strength and distance, calculate voltage: V=EdV = Ed
    3. If given voltage and electric field strength, calculate distance: d=VEd = \frac{V}{E}
  • Pay attention to units when solving problems
    • Electric field strength typically measured in V/m or N/C
    • Voltage measured in V
    • Distance usually measured in m (uniform field between charged plates)
  • When solving problems, identify given variables and unknown variable, then use appropriate equation to solve for unknown

Key Terms to Review (21)

Conservation of Energy: Conservation of energy is a fundamental principle in physics that states the total energy of an isolated system remains constant, it is said to be conserved over time. Energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another.
Coulomb: Coulomb is the fundamental unit of electric charge, named after the French physicist Charles-Augustin de Coulomb. It is a measure of the amount of electric charge and is a crucial concept in understanding various topics in electricity and magnetism, such as static electricity, electric fields, electric potential, and the behavior of charged particles.
Coulomb force: Coulomb force, also known as the electrostatic force, is the force of attraction or repulsion between two charged particles. It follows an inverse-square law and is governed by Coulomb's law.
Elastic potential energy: Elastic potential energy is the energy stored in an object when it is deformed elastically, such as when a spring is stretched or compressed. It can be calculated using the formula $U = \frac{1}{2} k x^2$, where $k$ is the spring constant and $x$ is the displacement from equilibrium.
Electric Dipole: An electric dipole is a separation of positive and negative electric charges within a system, typically a pair of equal and opposite charges separated by a small distance. This separation of charges creates an electric field and potential that are fundamental to understanding various phenomena in electromagnetism.
Electric field lines: Electric field lines are visual representations of the electric field created by charges. These lines indicate the direction and strength of the field in space.
Electric Field Lines: Electric field lines are a visual representation of the direction and magnitude of an electric field. They depict the path that a positive test charge would take if placed in the electric field, providing a way to visualize and understand the properties of the field.
Electric potential: Electric potential is the amount of electric potential energy per unit charge at a point in an electric field. It is measured in volts (V).
Electric Potential: Electric potential is the amount of work required to move a unit positive charge from an infinite distance to a specific point in an electric field. It represents the potential energy per unit charge at a given location and is a scalar quantity, meaning it has magnitude but no direction.
Electric Potential Difference: Electric potential difference, also known as voltage, is the potential energy difference between two points in an electric field. It represents the work done per unit charge in moving a test charge between those two points and is a fundamental concept in understanding the behavior of electric fields and circuits.
Equipotential Surfaces: Equipotential surfaces are imaginary surfaces in an electric field where the electric potential is constant. These surfaces are perpendicular to the direction of the electric field and represent points of equal potential energy for a test charge placed within the field.
Law of conservation of energy: The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. The total energy in an isolated system remains constant over time.
Parallel plate capacitor: A parallel plate capacitor consists of two conductive plates separated by a dielectric material. It stores electrical energy in the electric field created between the plates.
Parallel Plate Capacitor: A parallel plate capacitor is a type of capacitor consisting of two conductive plates separated by an insulating material called a dielectric. This arrangement creates an electric field between the plates, allowing the capacitor to store electrical energy.
Potential Energy: Potential energy is the stored energy an object possesses due to its position or state, which can be converted into kinetic energy or other forms of energy. This term is central to understanding various physical phenomena and energy transformations in the context of introductory college physics.
Uniform Electric Field: A uniform electric field is a region of space where the electric field vectors have the same magnitude and direction at all points. This means the electric field lines are parallel and evenly spaced, creating a constant electric field throughout the region.
Useful work: Useful work is the component of work that results in a desired outcome or effective energy transfer. It excludes any energy dissipated as waste, such as heat.
Vector: A vector is a quantity that has both magnitude and direction. It is typically represented by an arrow where the length represents the magnitude and the arrowhead points in the direction.
Volt: A volt is the unit of electric potential difference, which measures the amount of electric potential energy per unit charge between two points in an electric circuit. It helps us understand how much energy is available to move electric charges through a conductor, connecting it to concepts like power, energy storage, and circuit behavior.
Voltage: Voltage, also known as potential difference, is the electrical potential energy difference between two points in an electrical circuit. It is the driving force that causes the flow of electric current, and it is measured in units of volts (V).
Work: Work is a measure of the energy transferred by a force acting on an object as it is displaced. It is the product of the force applied and the distance moved in the direction of the force. Work is a fundamental concept in physics that is central to understanding energy, power, and the laws of motion.
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