Glossary

19.3 Electrical Potential Due to a Point Charge

2 min read•june 18, 2024

is a key concept in electrostatics. It describes the energy per unit charge at a point in an . For a , the potential decreases with distance, following an inverse relationship.

Understanding helps us grasp how charges interact and move in electric fields. It's closely related to electric field strength, but while the field is a vector, potential is a quantity measured in volts.

Electric Potential of a Point Charge

Equation for electric potential

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  • Electric potential (VV) at a point due to a (qq) given by the equation: V=kqrV = \frac{kq}{r}
    • kk is ###'s_Constant_0###, equals 8.99×109N⋅m2C28.99 \times 10^9 \frac{N \cdot m^2}{C^2}
    • qq is magnitude of point charge in coulombs (C)
    • rr is distance from point charge to point of interest in meters (m)
  • Electric potential is quantity, measured in volts (V) or joules per coulomb (J/C)
  • Potential inversely proportional to distance from point charge
    • As distance increases, potential decreases ()
  • Points of equal potential form an around the point charge

Electric potential vs electric field

  • Electric potential and electric field related but distinct concepts
  • Electric field (E⃗\vec{E}) is vector quantity describes force per unit charge at a point in space
    • Measured in newtons per coulomb (N/C) or volts per meter (V/m)
    • Electric field points in direction of force on positive test charge
  • Electric potential (VV) is scalar quantity describes potential energy per unit charge at a point in space
    • Measured in volts (V) or joules per coulomb (J/C)
    • Electric potential independent of direction of force
  • Electric field is negative of electric potential: E⃗=−∇V\vec{E} = -\nabla V
    • Electric field points in direction of decreasing potential
  • For point charge, both electric field and electric potential decrease with increasing distance from charge
    • Electric field decreases as 1r2\frac{1}{r^2}, while electric potential decreases as 1r\frac{1}{r} ()

Calculation of electric potential

  • To calculate electric potential at a point, use equation: V=kqrV = \frac{kq}{r}
  • Identify given values:
    1. Point charge magnitude (qq) in coulombs (C)
    2. Distance (rr) from point charge to point of interest in meters (m)
  • Substitute values into equation and solve for VV
  • Example: Find electric potential 2 meters away from point charge of 3 μ\muC
    • q=3×10−6q = 3 \times 10^{-6} C
    • r=2r = 2 m
    • V=(8.99×109N⋅m2C2)(3×10−6 C)2 m=13,485 VV = \frac{(8.99 \times 10^9 \frac{N \cdot m^2}{C^2})(3 \times 10^{-6} \text{ C})}{2 \text{ m}} = 13,485 \text{ V}

Work and Potential Difference

  • done to move a charge between two points is related to the
  • is the change in electric potential between two points
  • The applies to electric potential, allowing for the calculation of potential due to multiple point charges

Key Terms to Review (26)

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.
Coulomb's Constant: Coulomb's constant, also known as the electrostatic constant, is a fundamental physical constant that represents the strength of the electrostatic force between two point charges. It is a crucial parameter in understanding and describing various electromagnetic phenomena, including Coulomb's law, electric fields, and electrical potential.
Coulomb's Law: Coulomb's law is a fundamental principle in electrostatics that describes the force of interaction between two stationary electric charges. It establishes a mathematical relationship between the magnitude of the electrostatic force, the charges involved, and the distance between them.
Electric Field: The electric field is a vector field that describes the force experienced by a stationary, positive test charge at any given point in space. It represents the strength and direction of the electric force exerted on a charged particle by other charges in the vicinity, and is a fundamental concept in the study of electromagnetism and the behavior of charged particles.
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.
Equipotential Surface: An equipotential surface is a surface in an electric field where the electric potential is constant. In other words, all points on an equipotential surface have the same electric potential value.
Gradient: The gradient of a function is the rate of change of that function with respect to one or more of its independent variables. It represents the steepness or slope of a function at a particular point and is a fundamental concept in fields like physics, mathematics, and engineering.
Inverse Square Law: The inverse square law is a fundamental principle that describes how the strength or intensity of a force or property decreases with the square of the distance from the source. This law applies to various physical phenomena, including gravitational, electrical, and sound fields.
Joule: A joule is the SI unit of work or energy, equivalent to one newton-meter. It measures the amount of work done when a force of one newton displaces an object by one meter in the direction of the force.
Joule: The joule (J) is the standard unit of energy in the International System of Units (SI). It represents the amount of work done or energy expended when a force of one newton acts through a distance of one meter. The joule is a fundamental unit that connects various topics in physics, from work and energy to thermodynamics and electricity.
MicroCoulomb: A microCoulomb (μC) is a unit of electric charge in the International System of Units (SI). It is one-millionth of a Coulomb, which is the base unit of electric charge. The microCoulomb is commonly used to measure small amounts of electric charge, particularly in the context of electrical potential and electrostatic interactions.
Newton: The newton (N) is the standard unit of force in the International System of Units (SI). It is named after the famous English physicist Sir Isaac Newton, who made significant contributions to the understanding of the concept of force and its role in the laws of motion.
Point charge: A point charge is a hypothetical charge located at a single point in space with no physical size or structure. It is used to simplify the analysis of electric fields and forces in electrostatic problems.
Point Charge: A point charge is an idealized model of an electric charge that is considered to be concentrated at a single point in space, with no spatial extent. It is a fundamental concept in electrostatics and is used to understand the behavior of electric fields and electrical potential around charged objects.
Potential difference: Potential difference is the work done to move a unit charge between two points in an electric field. It is measured in volts (V) and often referred to as voltage.
Potential Difference: Potential difference, also known as voltage, is the measure of the work required to move an electric charge between two points in an electric field. It represents the difference in electric potential energy between two locations, and is a fundamental concept in understanding the behavior of electric circuits and the flow of electric current.
Scalar: A scalar is a physical quantity that has only magnitude and no direction. Examples include mass, temperature, and electric potential.
Scalar: A scalar is a physical quantity that has only a magnitude, or numerical value, and no direction. Scalars are contrasted with vectors, which have both a magnitude and a direction. Scalars are commonly used in physics to describe various physical properties and quantities.
Superposition Principle: The superposition principle states that when two or more waves or fields interact, the resulting wave or field is the vector sum of the individual waves or fields. This principle applies to various physical phenomena, including sound interference, electric fields, and electrical potential.
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.
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.
Voltmeter: A voltmeter is an electronic instrument used to measure the potential difference, or voltage, between two points in an electrical or electronic circuit. It is a crucial tool for understanding and analyzing electrical systems across various contexts, including the study of electrical potential, electric hazards, and the operation of DC circuits.
Voltmeters: Voltmeters are instruments used to measure the electrical potential difference, or voltage, between two points in an electric circuit. They are connected in parallel with the component across which the voltage is to be measured.
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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