Short Answer 
Coulomb’s Law describes the electric force between two charged objects using the formula F = k * (q‚ÇÅ * q‚ÇÇ) / r¬≤. To find the charge q‚ÇÅ that would result in no net force on another charge q‚ÇÇ, the total electric forces acting on q‚ÇÇ from two charged sources are set to zero, leading to the solution that q‚ÇÅ must equal 8nC.
Step 1: Understand Coulomb’s Law
Coulomb’s Law describes the force between two charged objects. The formula is expressed as:
- F = k * (q₁ * q₂) / r²
Here, F is the electric force, k is a proportionality constant, q‚ÇÅ and q‚ÇÇ are the magnitudes of the charges, and r is the distance between them. Understanding this formula is crucial for solving problems related to electric forces and charges.
Step 2: Set Up the Problem with Given Conditions
In this scenario, we need to determine the charge q‚ÇÅ such that another charge q‚ÇÇ feels no net electric force. We account for the forces acting on q‚ÇÇ from two charges:
- Charged at 20 cm distance, q‚ÇÅ
- Charged at 10 cm distance, -2nC
The total force equation that results from these interactions is set to zero:
- F = k * (q₁ * q₂) / (20 cm)² + k * (-2nC * q₂) / (10 cm)² = 0
Step 3: Solve for the Value of q‚ÇÅ
To find the value of q‚ÇÅ, we simplify our equation, leading to:
- (20 cm)² * q₁ + (10 cm)² * (-2nC) = 0
- From this, we can isolate q‚ÇÅ:
- q₁ = 2nC * ((10 cm)² / (20 cm)²) = 8nC
This calculation shows the required charge value, helping us understand how different charges interact through electric forces.