Overview
This lecture reviews how to calculate electric fields from point charges, emphasizing vector addition and the use of Coulomb’s law in determining field direction and magnitude.
Review of Forces Between Point Charges
- For multiple point charges, use Coulomb’s law to find the force each exerts and add as vectors for the total force.
- In a worked example, combined forces on a third charge yielded a specific magnitude and angle based on vector addition.
Introduction to Electric Field
- The electric field at a point describes the force a positive test charge would feel at that spot, divided by the charge's magnitude.
- The direction of the electric field is the direction a positive charge would be pushed; a negative charge feels force opposite to the field.
Calculating Electric Field from Point Charges
- The electric field from a single point charge is ( E = \frac{kQ}{r^2} ) in the direction away from positive and toward negative charges.
- The vector ( r ) points from the source charge to the measurement location.
Superposition Principle for Multiple Charges
- For several point charges, the total electric field is the vector sum of fields from each charge at the given location.
- Calculate each field separately, then combine using vector addition.
Electric Field at Infinity
- The electric field decreases as ( 1/r^2 ) and approaches zero as distance from the charges becomes extremely large.
- This is a standard convention for dealing with fields at infinity.
Key Terms & Definitions
- Coulomb's Law — Law giving the force between two point charges: ( F = \frac{k Q_1 Q_2}{r^2} ).
- Electric Field (E) — Force per unit charge experienced by a test charge: ( E = \frac{F}{q} ).
- Superposition Principle — The total electric field is the vector sum of fields from each charge.
- r-hat (( \hat{r} )) — A unit vector pointing from the source charge to the field point.
Action Items / Next Steps
- Practice example problems adding electric fields from multiple point charges.
- Review vector addition for electric fields.
- Prepare for further discussion or coursework on electric fields in advanced physics.