10.3 Electric Field Lines

Electric field lines (also known as lines of force) are a visual tool used to represent the direction and strength of an electric field in space. Introduced by Michael Faraday, they provide an intuitive way to map out the invisible electric field around charged objects.

Definition and Representation

• An electric field line is a curve drawn in such a way that the tangent to it at any point gives the direction of the electric field vector ($\vec{E}$) at that point.
• They are used to visualize the path that a small, positive "test charge" would take if it were free to move in the electric field.

Properties and Rules for Drawing Electric Field Lines

1. Origin and Termination: Electric field lines originate on positive charges and terminate on negative charges. If there is an excess of one type of charge, some lines will begin or end at infinity.
2. Direction: The arrow on a field line indicates the direction of the force on a positive test charge. Thus, lines point radially outward from a positive point charge and radially inward toward a negative point charge.
3. Strength of the Field: The density of the field lines (how close they are to each other) in a region represents the strength of the electric field.
   • Where the lines are close together, the electric field is strong.
   • Where the lines are far apart, the electric field is weak.
4. Lines Never Intersect: Electric field lines can never cross each other. If they did, it would imply that the electric field has two different directions at the same point, which is physically impossible.
5. Proportionality to Charge: The number of lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge.

Common Electric Field Patterns

• Electric Dipole: An electric dipole consists of two equal and opposite charges. The field lines originate on the positive charge and curve around to terminate on the negative charge.
• Two Like Charges: For two positive charges, the field lines emerge from each charge and curve away from each other, creating a neutral point in the middle where the electric field is zero. A neutral point is a location where the net electric field intensity is zero — the field vectors from the two source charges are equal in magnitude and opposite in direction, canceling each other out.
• Uniform Electric Field: Between two large, oppositely charged parallel plates, the electric field lines are parallel, equally spaced, and point from the positive plate to the negative plate. This represents a uniform electric field, where the strength and direction are constant everywhere (except near the edges, where "fringing" occurs).

Summary Table