Electric Fields – How Charges Interact at a Distance

Introduction

Charges can push or pull each other without touching. The concept of an electric field helps us describe this clearly and predict what will happen around any charge distribution.

Background / Prerequisites

• Positive and negative charges.
• Coulomb’s law.

Core Concepts

• Electric field: force per unit positive charge.
• It is a vector quantity with magnitude and direction.
• Field lines provide an intuitive sketch of the field.

Detailed Explanation

• Definition: \(\vec{E} = \vec{F}/q\).
• Point charge: \(\vec{E} = k q / r^2 \hat{r}\).
• Field lines start on positive charges and end on negative charges.
• Parallel plate capacitors produce nearly uniform fields between plates.

Examples / Applications

• Single point charge field decreasing as 1/r^2.
• Electric dipole field with characteristic loops.
• Uniform field between large charged plates used in particle accelerators.

Common Mistakes & Tips

• Confusing direction for positive vs negative test charges.
• Treating field lines as physical objects rather than indicators.
• Forgetting that field at a point depends on all charges present.

Summary / Key Takeaways

• Electric field is a powerful way to describe electric forces.
• Field lines are a visual tool, not literal entities.
• Knowing the field lets you calculate forces on any charge instantly.

Further Reading / Related Topics

• Electric potential.
• Gauss’s law.
• Capacitance.