Overview
This lecture covers the concept of electric fields, their calculation, effects on charges, and problem-solving strategies for various configurations of point charges and electric fields.
Electric Field Basics
- The electric field (E) is defined as the electric force (F) on a test charge divided by the magnitude of the test charge: E = F/q.
- Electric field units are newtons per coulomb (N/C).
- The electric field is a vector; its direction depends on the charge type placed in it.
Behavior in Fields
- A positive test charge in an electric field accelerates in the field's direction.
- A negative test charge accelerates opposite to the field's direction.
- Electric fields are created by charges: fields point away from positive charges and toward negative charges.
Calculating Fields from Point Charges
- The electric field due to a point charge: E = kQ/r², where k = 9 × 10⁹ N·m²/C², Q is the charge, and r is the distance from the charge.
- Use very small test charges to avoid affecting the source charge’s field.
Field Direction Examples
- For a positive charge, field vectors at various points radiate outward (north, east, northeast, southeast, etc.).
- For a negative charge, field vectors point inward toward the charge from all surrounding points.
Problem-Solving Examples
- To find electric field magnitude at a point: E = F/q.
- For a suspended charge in an electric field: Equate electric and gravitational forces, mg = Eq, solve for mass m.
- For an accelerating electron in a field: Use F = ma = Eq, solve for E.
- The field at a distance from a point charge: E = kQ/r², use geometry (e.g., Pythagoras) for non-axial points.
Effects of Distance and Charge Magnitude
- Doubling the source charge doubles E; doubling the distance quarters E; reducing distance by a factor increases E by the square of that factor.
Superposition and Net Fields
- The net electric field at a point is the vector sum of individual fields from each charge.
- For two identical charges, the field is zero at the midpoint.
- If one charge doubles, set E₁ = E₂ and solve for the zero-field point.
Key Terms & Definitions
- Electric Field (E) — The force per unit charge experienced by a test charge placed in the field.
- Coulomb’s Law — The force between two point charges: F = kQ₁Q₂/r².
- Test Charge — A small positive charge used to measure electric field without disturbing it.
- Superposition Principle — The net electric field is the vector sum of fields from all charges.
Action Items / Next Steps
- Memorize key formulas: E = F/q and E = kQ/r².
- Practice drawing field vectors for both positive and negative charges.
- Review unit conversions for micro, milli, and nano coulombs.
- Solve additional problems involving multiple charges and field calculations.