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Electric Force on Charges

Source lecture(s): SC134 Lec2

Intuition

A charge placed in an existing field feels a force proportional to its charge magnitude.

Formal Definition

\[\vec{F} = q\vec{E}\]

Mathematical Formulation

For a dipole in uniform \(\vec{E}\): \(\vec{\tau} = \vec{p}\times\vec{E}\), \(U = -\vec{p}\cdot\vec{E}\).

Derivation

Definition of field; for a dipole integrate force on \(+q\) and \(-q\) separated by \(\vec{d}\).

Worked Example

Electron in \(1\,\text{N/C}\) field feels \(1.6\times10^{-19}\,\text{N}\) opposite to field direction.

Common Mistakes

  • Treating field as a force.
  • Getting dipole torque direction wrong.

Quiz

Q1. Does a negative charge move with or against the field?

Answer

Against the field.