Overview
This lecture discusses the electric field produced by an electric dipole, focusing on the field at a point along the axial line and simplifying the expression under certain approximations.
Electric Field of a Point Charge and Dipole
- A point positive charge at a distance r produces an electric field.
- For a dipole, electric field at a point along its axis involves contributions from both charges (positive and negative).
Calculation of the Electric Field on the Axial Line
- Distance from the point to positive charge: (r - a), where "a" is half the dipole length.
- Electric field from positive charge: proportional to q / (r - a)² in the direction of the dipole axis.
- Electric field from negative charge: similar, but in the opposite direction and distance is (r + a).
- The total electric field is the vector sum: E = Eâ‚Š + Eâ‚‹.
Simplifying the Dipole Electric Field Expression
- Algebraic expansion: E = [q/(r - a)²] - [q/(r + a)²].
- When r >> a, terms involving "a²" can be neglected for simplification.
- Final approximation: E ≈ (2a·q)/(r³) along the dipole axis.
Dipole Moment and Direction
- The electric dipole moment (p) is defined as p = 2a·q in the direction from negative to positive charge.
- The electric field direction (unit vector p̂) follows the dipole axis.
Key Terms & Definitions
- Electric dipole — Two equal and opposite charges separated by a distance.
- Dipole moment (p) — Vector: p = 2a·q, points from negative to positive charge.
- Axial line — Line passing through both charges of the dipole.
- Electric field (E) — Region around a charge where forces are exerted on other charges.
Action Items / Next Steps
- Review the derivation of the electric field due to a dipole along the axial line.
- Practice problems simplifying electric field expressions for r >> a.