Physics HL · Chapter 18: Electric and Magnetic Fields
18.1 Electric Charge, Coulomb Force, and Electric Field
Build electrostatics from charge properties through inverse-square force and field representations, including uniform fields between plates.
Estimated time: 42 minutes
Charge Properties and How Bodies Become Charged
Electric charge is conserved: in any interaction, total charge before equals total charge after. A second property is quantization: net charge appears in integer multiples of the elementary charge e. These two statements are not optional background facts; they are the strongest constraints you have when checking charging-by-contact and induction scenarios.
n is an integer for isolated charge transfer in ordinary matter models.
In conductors, many electrons are mobile while positive lattice ions stay fixed. That is why induction language focuses on electron redistribution rather than positive-charge motion. In insulators, charge movement is much harder, so local polarization dominates instead of free large-scale redistribution.
Electrostatic induction has a predictable sign pattern: the induced net charge ends up opposite the nearby external charging object after grounding and removal. The detailed path depends on electron flow to or from ground, but the conservation logic always resolves ambiguity.
Coulomb's Law and Superposition
Coulomb's law gives the force magnitude between point charges. Like charges repel and unlike charges attract. Distance scaling is inverse-square, so even modest geometry changes can dominate charge-size changes. If distance doubles, force falls by a factor of four.
F = k rac{|q_1 q_2|}{r^2},qquad k = 8.99 imes 10^9 mathrm{N,m^2,C^{-2}}
Direction is along the line joining the charges; sign is encoded by attraction vs repulsion.
With three or more charges, use superposition: compute each pair contribution at the target charge and add vectorially. Never add magnitudes unless vectors are already collinear with matching direction. Many two-mark losses come from scalar addition in non-collinear geometry.
Electric Field as Force Per Unit Positive Test Charge
ec{E}= rac{ ec{F}}{q_{ ext{test}}},qquad E = k rac{|Q|}{r^2}
Field direction is the direction a small positive test charge would accelerate.
Field lines are a directional map, not literal particle tracks. Density of lines represents field magnitude qualitatively. Around a single positive charge lines point outward; around a single negative charge they point inward. In multi-charge systems, lines bend because the local field is the vector sum of all contributors.
Between large parallel plates (away from edges), electric field is approximately uniform and points from positive plate to negative plate. This is one of the most useful idealizations in IB questions because force and acceleration become constant in that central region.
E = rac{V}{d}
Uniform-field approximation for parallel plates with potential difference V and separation d.
Important
Field is property of space due to source charges. Force is what happens when a specific charge is placed into that field.
Simulation: Electric Superposition Map
Adjust two source charges and inspect field vectors, potential, and force on a movable test charge in real time.
|E| at probe
2.03e+6 N/C
Potential Ve
3.09e+4 V
Force on test q
0.01 N
Field direction
-25.6 deg
Test Yourself
Two point charges +2.0 microC and +8.0 microC are 0.30 m apart. At what distance from the +2.0 microC charge is the net field zero along the line joining them?
Hint: Set kq1/x^2 = kq2/(0.30 - x)^2 and solve for x between the charges.