electric fields- streamlines

Electric Fields

Electric Field Lines

• A field line or a streamline indicates the direction of force on a test charge introduced into the field.

• Streamlines show only the direction of the vector field. They are tangential to the vector field.

Electric Field Lines for Two source Charges

• Electric Field Lines - Pattern of several lines that extend between the source charge and infinity.

• Pattern can include infinite no. of lines.

Negative SourcePositive Source

Rules for Drawing Electric Field Patterns

RULE 1 : Density of lines in patterns

Density of electric lines reveal that QC>QB>QA

Objects with greater charge create stronger electric fields.

Density of lines in patterns

• E is greatest at locations closure to the surface of charge.

Field Lines are closer to each to each other.

Field Lines are farther from each other.

• There is never a component of electric force which is directed parallel to the surface.

• The electric force, and thus the electric field, is always directed perpendicular to the surface of an object .

• Lines of force that leave the surface of an object, may alter its direction. Eg., for configurations of two or more charges.

RULE 2 : Draw the lines of force perpendicular to the surfaces of objects.

RULE 3 : Electric field lines should never cross.

Electric Field Lines for Configurations of

Two or More Charges

• KQ/R2 has to be performed twice at each location.

• Can be added in head-to-tail fashion to determine the resultant or net electric field vector at each location.

• The magnitude and direction of the electric field at each location is

simply the vector sum of the electric field vectors for each individual charge.

• The individual source charges in the configuration possess the same amount of charge.

• The pattern is symmetrical in nature & the number of lines emanating from a source charge or extending towards a source charge are the same.

• This reinforces that the density of lines surrounding any given source charge is proportional to the quantity of charge on that source charge.

Electric Field Lines for Configurations of

Two or More Charges

Electric Field Line Patterns for Objects with Unequal Charges

Summary

Electric field lines always extend from a positively charged object to a negatively charged object, from a positively charged object to infinity, or from infinity to a negatively charged object.

Electric field lines never cross each other.

Electric field lines are most dense around objects with the greatest amount of charge.

At locations where electric field lines meet the surface of an object, the lines are perpendicular to the surface.

STREAMLINES

• In case of 2D fields, let Ez = 0, streamlines are in z-constant plane.