Electric fields are the invisible forces surrounding charged particles. They describe how electric charges interact, pushing and pulling each other through space. Understanding electric fields is key to grasping the behavior of charged objects and their effects on one another.

This section covers the strength and direction of electric fields, field line diagrams, and the superposition principle. We'll explore how to calculate and visualize electric fields, and how multiple charges combine to create complex field patterns.

Electric Field

Strength and direction of electric fields

• Electric field ($\vec{E}$) vector quantity describes force per unit charge at a point in space
  • Measured in units of N/C or V/m
• For a point charge ($q$), electric field at distance $r$ given by Coulomb's law:
  • $\vec{E} = \frac{kq}{r^2}\hat{r}$
  • $k$ Coulomb's constant: $k = 8.99 \times 10^9 \text{ N} \cdot \text{m}^2 / \text{C}^2$
  • $\hat{r}$ unit vector pointing from charge to point of interest
• Direction of electric field depends on sign of charge:
  • Positive charges create electric fields pointing radially outward (protons)
  • Negative charges create electric fields pointing radially inward (electrons)
• Strength of electric field decreases with distance from charge ($1/r^2$ relationship)
  • Moving twice as far from charge reduces field strength by factor of 4
• Electric field of a charged sphere acts as if all charge concentrated at center (outside the sphere)
• The electrostatic force between charged particles is directly related to the electric field strength

Electric field line diagrams

• Electric field lines visual representation of electric field in a region
  • Field lines originate from positive charges and terminate on negative charges
  • Density of field lines indicates relative strength of electric field (more dense = stronger field)
  • Field lines never cross, implies multiple field directions at single point
• For single point charge:
  • Field lines extend radially outward for positive charge (isolated proton)
  • Field lines extend radially inward for negative charge (isolated electron)
• For two equal and opposite charges (electric dipole):
  • Field lines extend from positive charge to negative charge
  • Field lines more concentrated near charges, indicating stronger field (H2O molecule)
• For two equal charges of same sign:
  • Field lines extend radially outward from each charge
  • Field lines more separated in region between charges, indicating weaker field (two protons)
• Electric field lines provide qualitative understanding of field direction and relative strength
  • Do not show exact magnitude of field at any point
  • Useful for visualizing field patterns and understanding charge interactions
• Electric flux is a measure of the electric field passing through a given surface area

Superposition of multiple charges

• Electric field obeys principle of superposition:
  • Net electric field at a point due to multiple charges is vector sum of individual electric fields created by each charge
• To find net electric field ($\vec{E}_{net}$) at a point:
  1. Calculate electric field ($\vec{E}_1, \vec{E}_2, ...$) at point due to each charge individually using Coulomb's law
  2. Add individual electric field vectors to find net electric field:
     • $\vec{E}_{net} = \vec{E}_1 + \vec{E}_2 + ...$
• When adding electric field vectors:
  • Consider both magnitude and direction of each field
  • Use vector addition techniques (components, trigonometry) to find resultant field
• Superposition allows calculation of electric fields in complex charge distributions (multiple point charges, charged lines/planes)
  • Break problem into simpler parts by considering each charge separately
  • Combine individual fields using vector addition to find net field
• Superposition is a powerful tool for analyzing electric fields and forces in electrostatic systems (capacitors, particle accelerators)

Work and Potential Energy in Electric Fields

• Work done by electric field on a charged particle relates to change in its potential energy
• Electric potential energy is the energy stored in a system of charges due to their positions
• Equipotential surfaces are regions where the electric potential is constant
• Moving charges perpendicular to equipotential surfaces requires work against the electric field