Chapter 16: Electric Fields

Introduction to Electric Fields

Electric fields are fundamental concepts in physics, describing the influence that electric charges exert on each other at a distance. The electric field at a point in space is defined as the force per unit positive test charge placed at that point.

• Electric Field (E): A region around a charged object where other charges experience a force.

• Direction: The direction of the electric field is the direction of the force on a positive test charge.

• Formula: , where is the force on a test charge .

Electric Field Lines

Electric field lines, or lines of force, provide a visual map of the electric field in the space surrounding electric charges.

• Properties of Field Lines:

  • Begin on positive charges and end on negative charges.

  • Never cross each other.

  • The number of lines leaving or entering a charge is proportional to the magnitude of the charge.

  • The density of lines indicates the strength of the field.

• Uniform Electric Field: Represented by equally spaced, parallel lines (e.g., between parallel plates).

• Example: The field around a single positive charge radiates outward; for a dipole, lines emerge from the positive and enter the negative charge.

Conceptual Example: Drawing Electric Field Lines

• Common mistakes include field lines not starting/ending on charges, crossing lines, or incorrect proportionality to charge magnitude.

The Electric Field Inside a Conductor: Shielding

Conductors behave uniquely under electrostatic conditions due to the mobility of their charges.

• Key Properties:

  • Excess charge resides on the surface of a conductor.

  • The electric field inside a conductor is zero at equilibrium.

  • Conductors shield their interiors from external electric fields (Faraday cage effect).

  • The electric field just outside a conductor is perpendicular to the surface.

• Example: A charge placed at the center of a hollow conductor induces an equal and opposite charge on the inner surface and an equal charge of the same sign on the outer surface.

Chapter 17: Electric Potential

Potential Energy in Electric and Gravitational Fields

Potential energy is the energy stored due to the position of an object in a force field. The concept is analogous for gravitational and electric fields.

• Gravitational Potential Energy:

• Electric Potential Energy:

• Both gravitational and electric forces are conservative, so the work done is path-independent.

The Electric Potential Difference

The electric potential at a point is the electric potential energy per unit charge at that point. The potential difference (voltage) between two points is the work done per unit charge to move a test charge between those points.

• Definition:

• Potential Difference:

• SI Unit: Volt (V), where

Common Usages of Electric Potential

Van de Graaff Generator

A Van de Graaff generator is a device that uses a moving belt to accumulate very high voltages on a hollow metal sphere. It is often used as a particle accelerator in physics experiments.

• Key Components: Hollow metallic sphere, moving belt, rollers, electrodes.

• Operation: Charges are transferred to the sphere, creating a large potential difference.

Work, Potential Energy, and Electric Potential: Example

• Given: ,

• Find:

• Potential difference:

Acceleration of Charges in Electric Fields

• A positive charge accelerates from higher to lower potential.

• A negative charge accelerates from lower to higher potential.

Electric Potential Energy in Total Energy

• Total energy can include translational, rotational, gravitational, elastic, and electric potential energies:

• Electron Volt (eV): (not an SI unit, but commonly used in atomic and particle physics).

Van de Graaff Example Calculation

• Change in electric potential energy:

• Kinetic energy gained:

• Final speed:

• Gravitational potential energy is negligible compared to electric potential energy for electrons.

Potential Difference in a Parallel-Plate Capacitor

• For a uniform field:

• Work done:

Electric Potential Difference Created by Point Charges

• Potential due to a point charge:

• Potential difference between two points:

• For multiple charges, potentials add algebraically.

Example: Potential of a Point Charge

• For at :

• For at :

Example: Total Electric Potential from Multiple Charges

• Sum the potentials from each charge at the point of interest.

• Example: For two charges and separated by , the potential at the midpoint is .

Potential Zero Points for Dipoles

• On the perpendicular bisector (mid-plane) of an electric dipole, the potential is zero everywhere.

• For charges and , the total potential is zero at two points along the line joining the charges, found by solving .