Overview
This lecture covers the fundamentals of electric fields, how to calculate them for point charges, directions for positive and negative charges, and detailed problem-solving involving electric field magnitudes and directions in various scenarios.
Electric Field Fundamentals
- 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 ).
- SI units of electric field are newtons per coulomb (N/C).
- Electric field is a vector, indicating both magnitude and direction.
- Positive test charges accelerate in the same direction as the electric field; negative charges accelerate opposite to the field.
- Electric fields are created by charges: away from positive charges, toward negative charges.
Calculating Electric Fields
- Electric field from a point charge: ( E = kQ/r^2 ), where ( k = 9 \times 10^9 ) N·m²/C².
- Direction: Draw an arrow from the charge to the point of interest (positive) or from the point to the charge (negative).
- Microcoulomb (μC) = ( 10^{-6} ) C, Nanocoulomb (nC) = ( 10^{-9} ) C, Millicoulomb (mC) = ( 10^{-3} ) C.
- Use vector addition for multiple charges' electric fields.
Electric Field and Forces Problem Examples
- To find field direction, use the behavior of positive/negative test charges in fields.
- Calculating magnitude: ( E = F/|q| ).
- For uniform fields (parallel plates): balance electric and gravitational forces for equilibrium (( Eq = mg )).
- For moving charges: use ( F = ma ) and ( F = Eq ) to find acceleration (( a = Eq/m )), or velocity via kinematic equations.
Multi-Charge & Location Problems
- The net electric field at a point is the sum of fields from each charge.
- For symmetric setups (equal and opposite charges), fields may cancel at specific points.
- If distances or charges change, recalculate using ( E \propto Q/r^2 ).
- The point where the net field is zero can be found algebraically by setting field magnitudes equal and solving for position.
Key Terms & Definitions
- Electric Field (E) — Force per unit charge, ( E = F/q ), in N/C.
- Coulomb’s Law — The force between two charges, ( F = kQ_1Q_2/r^2 ).
- Point Charge — An idealized charge at a single point in space.
- Test Charge — A small charge used to measure the electric field.
- Superposition Principle — Net field is the vector sum of fields from all charges.
- Uniform Electric Field — Field strength and direction are constant (e.g., between parallel plates).
Action Items / Next Steps
- Review example calculations for different charge arrangements and distances.
- Memorize fundamental constants: ( k, e, ) and masses/charges for electrons and protons.
- Practice solving problems involving electric field direction and magnitude.
- Prepare for homework on electric fields and force calculations.