Electric field lines are a visual tool for showing the direction and relative strength of an electric field. This cheat sheet helps students draw and interpret field lines for charges, conductors, and common charge arrangements. It is useful because many physics problems require connecting diagrams to force, field strength, and electric potential.
Clear rules prevent common errors such as crossing lines or drawing field lines inside conductors at electrostatic equilibrium.
The electric field direction is the direction a positive test charge would accelerate, so field lines point away from positive charges and toward negative charges. The electric field from a point charge has magnitude , and the electric force on a charge is . Closer field lines mean a stronger field, while evenly spaced parallel lines represent a uniform electric field.
Electric field lines are always perpendicular to conducting surfaces and to equipotential surfaces in electrostatic equilibrium.
Key Facts
- Electric field lines point in the direction of the force on a positive test charge, so for a positive test charge.
- Field lines begin on positive charges and end on negative charges, or they extend to infinity if there is no opposite charge nearby.
- The electric field strength from a point charge is , where .
- The electric force on a charge in an electric field is , and the force reverses direction if is negative.
- Electric field lines never cross because a single point in space cannot have two different electric field directions at the same time.
- A greater density of field lines represents a stronger electric field, so closely spaced lines mean a larger value of .
- In a uniform electric field, field lines are straight, parallel, and evenly spaced, and the potential difference satisfies when displacement is along the field.
- For a conductor in electrostatic equilibrium, inside the conducting material and field lines meet the surface at .
Vocabulary
- Electric field
- The electric field is the force per unit positive charge at a location, written as .
- Electric field line
- An electric field line is a drawn curve whose tangent shows the direction of at each point.
- Positive test charge
- A positive test charge is a small imaginary charge used to define the direction of an electric field without noticeably changing the field.
- Uniform electric field
- A uniform electric field has the same magnitude and direction everywhere, often shown by straight parallel lines.
- Equipotential surface
- An equipotential surface is a surface where electric potential is the same at every point, so moving along it requires no electric work.
- Electrostatic equilibrium
- Electrostatic equilibrium is the condition in which charges in a conductor are at rest and the electric field inside the conductor is .
Common Mistakes to Avoid
- Drawing field lines from negative charges and into positive charges is wrong because electric field direction is defined by the force on a positive test charge.
- Letting field lines cross is wrong because each point can have only one electric field vector direction.
- Spacing field lines evenly around unequal charges is wrong because the number and density of lines should reflect relative charge size and field strength.
- Drawing electric field lines parallel to a conductor surface in electrostatic equilibrium is wrong because the field must be perpendicular to the surface.
- Assuming electric potential always increases in the direction of field lines is wrong because electric field points in the direction of decreasing potential, described by .
Practice Questions
- 1 A point charge has . What is the electric field magnitude at a point away?
- 2 A charge of is placed in a uniform field of to the right. What is the magnitude and direction of the electric force on the charge?
- 3 Two large parallel plates create a uniform electric field of across a distance of . What is the magnitude of the potential difference between the plates?
- 4 A metal sphere is in electrostatic equilibrium with extra negative charge on it. Explain where the excess charge is located, what the electric field is inside the metal, and how field lines meet the surface.