Electric Force and Electric Field: Applications in Calculations

Overview

• Applying concepts of electric force and electric field to calculate:
  • Net electric field or force on a point charge by a system of charges.
  • Electric field due to a system of point charges using Coulomb's Law and superposition principle.

Key Formulas and Concepts

Coulomb's Law

• Measures force interaction between point charges.
• Formula: ( F = k \frac{q_1 q_2}{r^2} )
  • ( k ) is Coulomb's constant ( = 8.988 \times 10^9 \text{N m}^2/\text{C}^2 )
  • Unit for electric force: Newtons (N)

Electric Field

• Imaginary field surrounding a charge.
• Formula for electric field due to a point charge: ( E = \frac{F}{q} )
  • Unit: Newton per Coulomb (N/C)

Assigning Point Reference

• Important for determining the direction of electric forces.

Example Problems

Problem 1: Electric Force Between Charges

• Given: Two charges, Q1 (200 µC) and Q2 (100 µC), 1 meter apart.
• Calculation:
  • Force at Q1 due to Q2: ( F = k \frac{200 \times 10^{-6} \times 100 \times 10^{-6}}{1^2} = 180 \text{N} )
  • Direction: Repulsion (like charges)

Problem 2: Forces on a Third Charge (Q3)

• Setup: Q1, Q2, and Q3 arranged linearly.
• Calculate force interactions:
  • Between Q2 and Q3: Attraction due to opposite charges.
  • Between Q1 and Q3: Calculate vector sum.

Problem 3: Net Electric Force on Fourth Charge (Q4)

• Setup: Charges at corners of a square.
• Use vector addition and Pythagorean theorem to find net force on Q4.
• Calculation involves finding diagonal distances and angles using trigonometry.

Electric Field Calculations

Problem 4: Electric Field at a Point P

• Given: Charge Q1 (50 nC) at a distance of 1m.
• Calculation:
  • ( E_1 = k \frac{50 \times 10^{-9}}{1^2} = 450 \text{N/C} )
• Net electric field: Sum of vector fields from different charges.

Problem 5: Net Electric Field at a Point with Two Charges

• Setup: Charges Q1 and Q2 at different distances.
• Compute net field: Use vector subtraction if fields are opposite.

Problem 6: Electric Field in a Plane

• Given: E-fields from multiple charges.
• Calculation: Use Pythagorean theorem to find the resultant electric field magnitude.
• Determine direction using angle calculations with respect to the axis.

Conclusion

• Procedures for computing net electric force and field involve:
  • Recalling formulas.
  • Assigning point references.
  • Calculating forces and fields as vectors.
  • Using principles of superposition, vector addition, and trigonometry for precise results.
• For questions, contact the lecturer.