Electric Charges, Forces, and Fields

19-1 Electric Charge

Electric charge is a fundamental property of matter that gives rise to electric forces and fields. The effects of electric charge were first observed as static electricity, such as when an amber rod rubbed with fur attracts small objects. There are two types of electric charge: positive and negative. Like charges repel each other, while opposite charges attract.

• Electron Charge: All electrons have the same charge, denoted as e. The proton has the same magnitude of charge but the opposite sign.

• SI Unit: The unit of electric charge is the coulomb (C).

• Charge Conservation: The total electric charge in the universe is constant; charge is conserved.

• Charge Quantization: Electric charge exists in discrete units of e.

• Ions: Atoms that lose electrons become positive ions; those that gain electrons become negative ions.

• Polarization: Some materials can become polarized, meaning their atoms rotate in response to an external charge, allowing a charged object to attract a neutral one.

19-2 Insulators and Conductors

Materials are classified based on their ability to allow electrons to move:

• Conductors: Materials (usually metals) whose conduction electrons are free to move throughout. Excess charge on a conductor is distributed over its surface.

• Insulators: Materials (usually nonmetals) whose electrons seldom move from atom to atom.

• Semiconductors: Materials with properties intermediate between conductors and insulators; their conductivity changes with chemical composition.

• Photoconductive Materials: Become conductors when exposed to light.

19-3 Coulomb’s Law

Coulomb’s law describes the force between two point charges. The force acts along the line connecting the charges and is attractive for opposite charges, repulsive for like charges.

• Formula: where F is the force, q1 and q2 are the charges, r is the distance between them, and k is Coulomb’s constant.

• Action-Reaction: The forces on the two charges are equal and opposite.

• Superposition Principle: For multiple point charges, the forces add as vectors.

• Spherical Distributions: Coulomb’s law applies to spherically symmetric charge distributions, analogous to gravity for spherical masses.

19-4 The Electric Field

The electric field is a region around a charged object where electric forces are exerted on other charges. It is defined as the force per unit charge.

• Definition: where \vec{E} is the electric field, \vec{F} is the force, and q is the test charge.

• SI Unit: Newton per coulomb (N/C).

• Direction: The force on a positive charge is in the direction of the field; for a negative charge, it is opposite.

• Point Charge Field: The field points radially away from a positive charge and toward a negative charge.

• Superposition: Electric fields from multiple charges add as vectors.

19-5 Electric Field Lines

Electric field lines are a visual tool to represent the direction and strength of the electric field.

• Properties:

  • Point in the direction of the field vector at every point.

  • Start at positive charges or infinity; end at negative charges or infinity.

  • Are denser where the field is stronger.

• Field Line Density: The number of lines is proportional to the magnitude of the charge.

• Combinations: Field lines for multiple charges show regions of strong and weak fields; only at certain points is the field zero.

• Parallel-Plate Capacitor: Consists of two conducting plates with equal and opposite charges, creating a uniform electric field between them.

19-6 Shielding and Charging by Induction

Conductors exhibit unique behaviors regarding electric charge and fields:

• Surface Charge: Excess charge on a conductor resides on its surface.

• Zero Internal Field: The electric field inside a conductor is zero when charges are at rest.

• Field Perpendicularity: The electric field is always perpendicular to the surface of a conductor.

• Curvature: The field is stronger where the surface is more sharply curved.

• Charging by Induction: A conductor can be charged by induction if grounded, allowing like charges to leave. If isolated before removing the inducing rod, only excess charge remains.

19-7 Electric Flux and Gauss’s Law

Electric flux quantifies the electric field passing through a surface. Gauss’s law relates electric flux to the charge enclosed by a surface.

• Electric Flux: where \Phi_E is the electric flux, \vec{E} is the electric field, and \vec{A} is the area vector.

• Gauss’s Law: where Q_{enc} is the charge enclosed, and \varepsilon_0 is the permittivity of free space.

• Applications: Gauss’s law is useful for finding electric fields in systems with simple symmetry.

Summary Table: Key Concepts of Chapter 19

Example: Charging by Induction

When a neutral conductor is brought near a charged rod and grounded, electrons move to or from the ground, leaving the conductor charged when the ground connection is removed.

Example: Electric Field of a Point Charge

The electric field at a distance r from a point charge q is given by:

Example: Application of Gauss’s Law

For a spherical charge distribution, Gauss’s law can be used to find the electric field outside the sphere, treating the charge as if it were concentrated at the center.