UY1: Steps to solving problems involving Coulomb’s Law

Identify the relevant concepts: 
Coulomb’s law describes the electric force between charged particles.

Set up the problem using the following steps:

  1. Sketch the locations of the charged particles and label each particle with its charge.
  2. If the charges do not all lie on a single line, set up an xy-coordinate system.
  3. The problem will ask you to find the electric force on one or more particles. Identify which these are.

Execute the solution as follows:

  1. For each particle that exerts an electric force on a given particle of interest, use $F = k \frac{|q_{1} q_{2}|}{r^{2}}$ to calculate the magnitude of that force.
  2. Using those magnitudes, sketch a free-body diagram showing the  electric force vectors acting on each particle of interest. The force exerted by particle 1 on particle 2 points from particle 2 toward particle 1 if the charges have opposite signs, but points from particle 2 directly away from particle 1 if the charges have the same sign.
  3. Use the principle of superposition to calculate the total electric force – a vector sum – on each particle of interest.
  4. Use consistent units; SI units are completely consistent.
  5. Some problems involve continuous distributions of charge along a line, over a surface, or throughout a volume. In these cases, the vector sum in step 3 becomes a vector integral. We divide the charge distribution into infinitesimal pieces, use Coulomb’s law for each piece, and integrate to find the vector sum. Sometimes this can be done without actual integration.
  6. Exploit any symmetries in the charge distribution to simplify your problem solving. For example, two identical charges q exert zero net electric force on a charge Q midway between them, because the forces on Q have equal magnitude and opposite direction.

Evaluate your answer: Check whether your numerical results are reasonable. Confirm that the direction of the net electric force agrees with the principle that charges of the same sign repel and charges of opposite sign attract.

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