Overview
This lecture demonstrates how to calculate the net force on a charge using Coulomb's Law, vector addition, and component breakdown for multiple point charges.
Problem Setup
- Three charges are positioned at (1,0), (2,2), and (3,1) meters.
- Two blue charges are +1 C at (1,0) and (2,2); a red charge is -2 C at (3,1).
- The goal is to find the total force on the -2 C charge from the two +1 C charges.
Calculating Individual Forces
- Use Coulomb's Law: ( F = k \frac{|q_1 q_2|}{r^2} ), where ( k = 8.99 \times 10^9 ) N·m²/C².
- Distance between (1,0) and (3,1) is ( \sqrt{5} ) meters; angle is 26.6° above the x-axis.
- Distance between (2,2) and (3,1) is ( \sqrt{2} ) meters; angle is 45° below the x-axis.
- Force from charge at (1,0) on (3,1) is ( -3.6 \times 10^9 ) N (attractive, toward (1,0)).
- Force from charge at (2,2) on (3,1) is ( -9 \times 10^9 ) N (attractive, toward (2,2)).
Vector Addition of Forces
- Forces are vectors and must be summed using components.
- Break each force into x and y components using cosine and sine of their respective angles.
- Add corresponding x and y components, carefully tracking negative signs for direction.
- The resulting net force is approximately 9.58 GN (giga-newtons) in the negative x-direction and 4.74 GN in the positive y-direction.
Final Result and Direction
- Net force points up and to the left, closer to charge 2 due to its stronger pull (smaller distance).
- Magnitude of the net force is about 10.7 GN at 26.4° above the negative x-axis.
- Process relies heavily on vector addition and prior knowledge of vector components.
Key Terms & Definitions
- Coulomb's Law — The law that calculates electrostatic force between two point charges: ( F = k \frac{|q_1 q_2|}{r^2} ).
- Vector Addition — The process of combining vectors by adding their components to find a resultant vector.
- Component Breakdown — Splitting a vector into its horizontal (x) and vertical (y) components.
Action Items / Next Steps
- Review physics principles on vector components and vector addition.
- Prepare for shortcut methods to handle large numbers in future lessons.