AP® Physics 2: Algebra-Based · Unit 10 · Topic 10.3
Field Lines and Superposition
Every charge makes its own field everywhere in space, and the total field at any point is just the vector sum of each charge's contribution. Field lines are a picture of that sum, redrawn instantly because the fields themselves exist everywhere all along, not just where you look.
A field line is a map of direction, not a thing that physically exists. At every point in space, each charge nearby contributes its own field vector, pointing away from positive charges and toward negative ones, falling off as 1/r2. The actual field at that point is the vector sum of all those contributions. When you drag a charge, nothing travels across the room to update the lines, the field was already defined by the new positions everywhere, instantly, so the whole pattern simply reflects the new sum.
For a dipole, one positive and one negative charge, lines leave the positive charge and curve around to end on the negative one. Where lines bunch close together, the field is strong, because the same number of lines is squeezed through a smaller area. Far from both charges the lines spread out and the field weakens fast. Superposition is also how you find special points like where the field cancels entirely: between a +4 nC and a +1 nC charge, the point of zero field sits closer to the smaller charge, since its weaker field only needs a shorter distance to match the stronger one.
This topic sets up the next one, electric potential, which is built from the same superposition idea but adds scalars instead of vectors, which is usually easier math. Keep field lines and potential separate in your head: lines show force direction, potential describes energy, and a charge's actual path depends on both the force at each instant and the velocity it has already built up.
Key terms
- Superposition
- The total field at a point is the vector sum of the fields each individual charge would produce there alone.
- Field line
- A curve whose direction at each point shows the direction of the electric force on a positive test charge there.
- Dipole
- A pair of equal and opposite charges separated by some distance, with field lines running from the positive to the negative charge.
- Field line density
- How tightly packed field lines are in a region, which indicates how strong the field is there.
Watch it explained
- How it worksHow do the fields of two separate charges add up as vectors at every point in space?
- How it worksDraw the field line pattern of a dipole and explain what the crowding of the lines means.
- Worked exampleFind the point on the line between a +4 nC and a +1 nC charge 0.30 m apart where the field is zero.
- Common mistakeWhy isn't a field line the actual path a released charge would travel along?
- Going furtherWhat does the field pattern look like for two equal positive charges instead of a dipole?
Check yourself
End of topic.