recall and use F = qE for the force on a charge in an electric field

Electric Fields and Field Lines ⚡️

What is an Electric Field?

An electric field E is a region around a charge where other charges feel a force. Think of it like an invisible wind that pushes or pulls on a tiny ball (the test charge).

Field Lines ✨

Field lines are a visual aid. They show the direction a positive test charge would move:

  • Lines start on positive charges and end on negative charges.

  • Closer lines mean a stronger field.

  • They never cross.

Force on a Charge: \$F = qE\$ 🔬

Here, q is the test charge (in coulombs) and E is the electric field (in newtons per coulomb).

  1. Identify the magnitude of the field E.

  2. Choose the test charge q (positive or negative).

  3. Multiply: \$F = qE\$.

  4. Direction: if q is positive, F points in the same direction as E; if negative, it points opposite.

SymbolMeaningUnits
\$q\$Charge of the test particleCoulombs (C)
\$E\$Electric field strengthNewtons per Coulomb (N/C)
\$F\$Force on the chargeNewtons (N)

Exam Tip 💡

When you see a problem asking for the force on a charge in a given field:

  1. Write down \$F = qE\$.

  2. Check the sign of q to determine direction.

  3. Remember units: N = C × N/C.

  4. Show your work clearly; even if the answer is correct, partial marks are awarded for correct steps.

Quick Practice Problem 🚀

A positive charge of +2 µC is placed in a uniform electric field of 5 kN/C pointing to the right. What is the magnitude and direction of the force?

Answer: \$F = (2\times10^{-6}\,\text{C})(5\times10^{3}\,\text{N/C}) = 10^{-2}\,\text{N}\$ to the right.