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The electric field E at position r due to a point charge q is E = kq/r² r̂, where r̂ is the unit vector from the charge. Field strength decreases as inverse square of distance; direction is radially outward for positive charge, inward for negative.
Plot field lines for single charges, then for multiple charges using superposition. Use field visualization software to develop intuition before calculations.
You already know from Coulomb's law that two charges exert forces on each other. The electric field is a conceptual upgrade that separates this interaction into two steps: first, a source charge *creates* a field that fills the surrounding space; second, any other charge placed in that field *feels* a force from the field at its location. The field exists independently — even if there is nothing there to feel it. This two-step picture is more than bookkeeping: it is physically necessary when charges are moving, because changes in the field propagate at the speed of light, not instantaneously.
For a point charge q, the field at position r is E = kq/r² r̂, where r̂ is the unit vector pointing away from the charge. The magnitude falls off as 1/r², matching Coulomb's law exactly — which makes sense, since the force on a test charge q₀ is F = q₀E. The direction encodes the sign of the source: positive charges produce field lines radiating outward (they would push a positive test charge away), while negative charges produce field lines pointing inward (a positive test charge would be pulled toward them). Always draw the direction as "what would happen to a positive test charge."
When multiple charges are present, you use the superposition principle from your prerequisite: add the vector contributions from each charge independently. This is what makes the electric field framework powerful. To find the field at a point due to three charges, compute three separate field vectors using E = kq/r² r̂ for each charge, then add them as vectors, component by component. The distance r and direction r̂ must be measured from each individual source charge to the field point — a common error is reusing the same r for all charges.
Field lines give a visual summary of the vector field. They point in the direction of E everywhere, their density is proportional to field strength, they begin on positive charges and end on negative charges, and they never cross. For a single positive charge the lines radiate symmetrically in all directions; for a positive–negative pair (a dipole) the lines curve from the positive to the negative charge. Visualizing these patterns before computing develops the intuition needed to check whether calculated results are physically reasonable — a calculated field pointing "the wrong way" usually signals a sign or direction error in the vector setup.