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UY1: Steps to solving problems involving Coulomb's Law

Use a reliable step-by-step method for Coulomb-force problems, including sign conventions, vector addition, and reasonableness checks.

  • University Physics Year 1
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Why this matters + quick links

This page gives the UY1 working model/result for Steps to solving problems involving Coulomb’s Law. You reuse it when you build fields/potentials by symmetry or superposition, and when you connect fields to forces, energy, and circuits.

1) At a glance

For Coulomb-force questions, use this workflow:

  1. Draw and label the charge configuration.
  2. Determine force directions from signs (attraction vs repulsion).
  3. Compute each pairwise force magnitude with Coulomb’s law.
  4. Add forces as vectors (components if needed).
  5. Check units, direction, and magnitude reasonableness.

Modelling context (what Coulomb’s law assumes):

  • Charges are treated as point charges (or spherically symmetric so they behave like point charges outside).
  • The configuration is electrostatic (charges fixed in place, no time-varying fields).
  • The medium is vacuum/air unless a different permittivity is stated.

Prerequisites: Coulomb’s Law, Electric Field Of A Point Charge, Mathematics for Undergraduate Physics
Next uses: Electric Dipole, Electric Potential Energy With Several Point Charges

2) Setup

Coulomb’s law magnitude between two point charges:

F = k|q₁q₂|/r², k = 1/4πε₀

Sign conventions and direction:

  • Like charges repel.
  • Unlike charges attract.
  • Force on charge A points along the line joining A and the source charge.

If geometry is 2D or 3D, set coordinates first and resolve vectors into components.

Common traps (signs, units, and vectors)
  • Keep magnitudes positive and put the direction into the vector unit direction (or component signs). Don’t try to carry “charge signs” inside the magnitude.
  • Convert units early: μC → 10⁻⁶ C, cm → 10⁻² m.
  • Superposition is vector: forces add as vectors, not as scalars.

3) Core derivation/explanation

For a target charge qₜ, each other charge qᵢ contributes a vector force vector F_(i → t). Use superposition:

vector F_(net on t) = ∑ᵢ vector F_(i → t)

Recommended execution order:

  1. Compute each distance rᵢ.
  2. Compute each magnitude Fᵢ = k|qᵢqₜ|/rᵢ².
  3. Assign direction (sign) using attraction/repulsion.
  4. Convert to components and sum:
Fₓ = ∑ᵢFᵢₓ, F_y = ∑ᵢF_iy
  1. Reconstruct net vector if needed:
| vector F| = square root of (Fₓ² + F_y²), θ = tan⁻¹ (F_y/Fₓ)

For continuous charge distributions, replace the sum by an integral over dq.

Checks (sanity)

  • Symmetry: equal charges placed symmetrically often cancel one component of the net force.
  • Limits: as a separation r increases, that pairwise contribution must fall like 1/r².
  • Units: Coulomb force must be in newtons.

4) Worked example(s)

Three charges lie on the x-axis: q₁ = +2.0 μC at x = 0, q₂ = -1.0 μC at x = 0.30 m, and q₃ = +3.0 μC at x = 0.60 m. Find net force on q₂.

Force from q₁ on q₂ (attractive, toward left):

F_(1 → 2) = k|q₁q₂|/(0.30)² = 8.99 × 10⁹(2.0 × 10⁻¹²)/0.09 ≈ 0.200 N

Force from q₃ on q₂ (attractive, toward right):

F_(3 → 2) = k|q₃q₂|/(0.30)² ≈ 0.300 N

So net force on q₂ is:

Fₙₑₜ = 0.300-0.200 = 0.100 N

toward + x (right).

5) Practice set (with hints + answers)

  1. Two charges + q and + q are separated by r. Direction of force on left charge? Hint: like charges repel. Answer: leftward, away from the right charge.

  2. A force answer comes out in N m. What likely went wrong? Hint: check power of r in denominator. Answer: used 1/r instead of 1/r² (or unit conversion error).

  3. Why is a free-body diagram useful before calculation? Hint: sign errors are common. Answer: it fixes direction conventions before algebra and prevents vector-sign mistakes.

6) Summary + next steps

  • Coulomb problems are mostly about disciplined setup and vector bookkeeping.
  • Keep magnitudes positive, then apply direction explicitly.
  • Always run a final physical check: does direction match attraction/repulsion intuition?

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