Electric Charge and Electric Field

Learning Outcomes

This chapter introduces the foundational concepts of electric charge and electric field, which are essential for understanding electrostatics in physics. Students will learn to distinguish between electric force and electric field, visualize electric field lines, and calculate properties of charge distributions, including dipoles.

• Distinction between Electric Force and Electric Field: Understand how electric force acts between charges and how electric fields represent the influence of a charge in space.

• Electric Field Lines: Learn to use field lines to visualize and interpret electric fields.

• Charge Distributions: Calculate properties of various charge distributions, including dipoles.

Relationship to Maxwell’s Equations

Maxwell’s Equations in Electrostatics

Maxwell’s Equations are the fundamental laws governing all electromagnetic phenomena. In this chapter, the focus is on static charges and electric fields, particularly the first equation:

• Gauss’s Law:

• Symbols:

  • : Electric field

  • : Charge density

  • : Vacuum permittivity (a physical constant)

Other Maxwell equations (for reference):

Coulomb’s Law

Electric Force Between Point Charges

Coulomb’s Law quantifies the electric force between two point charges. The force is proportional to the product of the charges and inversely proportional to the square of the distance between them.

• Formula: where

  • : Magnitude of the electric force

  • : Coulomb’s constant ( N·m2/C2)

  • , : Charges

  • : Distance between charges

• Direction:

  • Like charges repel; force vectors point away from each other.

  • Opposite charges attract; force vectors point toward each other.

Electric Field: Introduction

Concept of Electric Field

The electric field is a region around a charged object where other charges experience a force. It is a way to describe how a charge modifies the properties of space around it.

• When two charges (A and B) are present, they exert forces on each other.

• If one charge (B) is removed, the remaining charge (A) still influences the space at the location where B was.

• This influence is described by the electric field created by A at that point.

Measuring Electric Field

The electric field at a point is defined as the force per unit charge exerted on a test charge placed at that point.

• Formula: where

  • : Electric field vector

  • : Force exerted on the test charge

  • : Test charge

• The direction of is the direction of the force on a positive test charge.

Electric Field of a Point Charge

Field Produced by a Point Charge

A point charge produces an electric field at all points in space. The field’s strength decreases with increasing distance from the charge.

• Formula: where

  • : Source charge

  • : Distance from the charge to the field point

  • : Unit vector pointing from the source charge to the field point

• For a positive charge, the field points away from the charge; for a negative charge, it points toward the charge.

Superposition of Electric Fields

Adding Electric Fields

The total electric field at a point due to multiple charges is the vector sum of the fields produced by each charge.

• Formula:

• Each field is calculated using the formula for a point charge and then added vectorially.

Electric Field Lines

Visualizing Electric Fields

Electric field lines are imaginary lines that represent the direction and strength of the electric field. The tangent to a field line at any point gives the direction of the field vector at that point.

• Field lines point away from positive charges and toward negative charges.

• The density of field lines indicates the magnitude of the field: closer lines mean a stronger field.

• Field lines never intersect.

Field Lines for Different Charge Configurations

• Point Charge: Field lines radiate outward (for positive) or inward (for negative).

• Dipole: Field lines emerge from the positive charge and terminate at the negative charge.

• Two Equal Positive Charges: Field lines repel from both charges and curve outward.

Electric Dipoles

Definition and Properties

An electric dipole consists of two equal and opposite charges separated by a distance. The dipole moment is a vector pointing from the negative to the positive charge.

• Dipole Moment: where

  • : Magnitude of each charge

  • : Vector from negative to positive charge

• Dipoles create characteristic field patterns, with field lines emerging from the positive and terminating at the negative charge.

Water Molecule as a Dipole

The water molecule is electrically neutral overall, but the arrangement of atoms causes a separation of charge, making it an electric dipole. This property is crucial for water’s role as a solvent in chemistry.

• Salt (NaCl) dissolves in water because the positive sodium and negative chloride ions are attracted to the respective ends of the water dipole.

• If water were not a dipole, it would be a poor solvent, and many chemical reactions in solution would not occur.

Force and Torque on a Dipole

Dipole in a Uniform Electric Field

When an electric dipole is placed in a uniform electric field, it experiences no net force but does experience a torque that tends to align the dipole with the field.

• Torque on a Dipole: where

  • : Torque

  • : Dipole moment

  • : Electric field

• This principle is used in classical calculations and can model quantum mechanical behavior in molecules.

Summary Table: Key Equations

Additional info: Some context and definitions have been expanded for clarity and completeness, including the role of water as a dipole and the significance of field lines in visualizing electric fields.