Ch. 21 | Electric Potential & Electric Potential Energy

Review: Coulomb’s Law and Electric Fields

Coulomb’s Law describes the force between two point charges, while the electric field is the force per unit charge at a point in space. These concepts are foundational for understanding electric potential and potential energy.

• Coulomb’s Law: The magnitude of the electric force between two point charges is given by: where , and are the charges, is the distance between them, and is the unit vector from one charge to the other.

• Electric Field from a Point Charge:

• Vector Components:

Drawing Electric Field Lines

Electric field lines provide a visual representation of the direction and strength of the electric field around charges.

• Field lines originate from positive charges (+Q) or infinity and terminate on negative charges (–Q) or extend to infinity.

• The number of field lines is proportional to the magnitude of the charge.

• The electric field vector is tangent to the field line at any point.

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

• Field lines never cross each other.

Work, Potential Energy, and Conservation of Energy

Work is done on a body when a force acts on it during displacement. If the force is conservative, the work can be expressed in terms of potential energy, and the process is reversible and path-independent.

• Work Done by a Constant Force:

• Conservative Forces: Work done is path-independent and reversible. Total work over a closed path is zero.

• Work-Energy Theorem: Work done on an object changes its kinetic energy:

• Conservation of Energy: If only conservative forces do work:

• Work and Potential Energy:

Electric Potential Energy

When a charged particle moves in an electric field, the field does work on the particle, which can be expressed as a change in electric potential energy (). This is analogous to gravitational potential energy.

• Electric Potential Energy in a Uniform Field:

• Potential energy increases if a test charge moves opposite to the electric force; it decreases if the charge moves in the direction of the force.

• The concept applies to any static charge distribution, not just uniform fields.

Electric Potential

Electric potential () is the potential energy per unit charge at a point in an electric field. It is a scalar quantity and provides a convenient way to describe energy changes for charges in electric fields.

• Definition: or

• SI Unit: Volt ()

• Relation to Electric Field:

Examples and Applications

• Potential Energy Change for Point Charges: For two point charges and separated by distance :

• Example Problem: A point charge is at . A second charge moves from infinity to . Find the change in potential energy and the initial velocity if its mass is .

Summary Table: Key Concepts