Find resultant force on 20ፀ if Q1=5ፀ, Q2=10ፀ and Q3=ፀ to distance of 30cm
To find the resultant force on a charge due to multiple charges, we need to calculate the individual forces due to each charge and then find the vector sum of those forces.
The formula to calculate the force between two charges is given by Coulomb's Law:
𝐹 = (𝑘 * 𝑄₁ * 𝑄₂) / 𝑟²
Where 𝐹 is the force between the charges, 𝑘 is the electrostatic constant (9 x 10^9 Nm²/C²), 𝑄₁ and 𝑄₂ are the magnitudes of the charges, and 𝑟 is the distance between the charges.
Let's calculate the forces due to each charge Q1, Q2, and Q3 on charge Q.
1. Force due to Q1:
𝐹₁ = (𝑘 * Q * Q₁) / 𝑟₁²
Given Q = 20ፀ, Q₁ = 5ፀ, and 𝑟₁ = 30cm = 0.3m
Substituting these values into the formula:
𝐹₁ = (9 x 10^9 Nm²/C² * 20ፀ * 5ፀ) / (0.3m)²
Simplifying the equation:
𝐹₁ = (9 x 10^9 Nm²/C² * 100ፀ²) / 0.09m²
𝐹₁ = 9 x 10^9 N * 100ፀ² / 0.09m²
𝐹₁ = 100 x 10^9 N * 100ፀ² / 0.09m²
𝐹₁ ≈ 111,111,111 N
2. Force due to Q2:
𝐹₂ = (𝑘 * Q * Q₂) / 𝑟₂²
Given Q = 20ፀ, Q₂ = 10ፀ, and 𝑟₂ = 30cm = 0.3m
Substituting these values into the formula:
𝐹₂ = (9 x 10^9 Nm²/C² * 20ፀ * 10ፀ) / (0.3m)²
Simplifying the equation:
𝐹₂ = (9 x 10^9 Nm²/C² * 200ፀ²) / 0.09m²
𝐹₂ = 9 x 10^9 N * 40000ፀ² / 0.09m²
𝐹₂ = 40000 x 10^9 N * 40000ፀ² / 0.09m²
𝐹₂ ≈ 177,777,778 N
3. Force due to Q3:
𝐹₃ = (𝑘 * Q * Q₃) / 𝑟₃²
Given Q = 20ፀ, Q₃ = 1ፀ, and 𝑟₃ = 30cm = 0.3m
Substituting these values into the formula:
𝐹₃ = (9 x 10^9 Nm²/C² * 20ፀ * 1ፀ) / (0.3m)²
Simplifying the equation:
𝐹₃ = (9 x 10^9 Nm²/C² * 20ፀ²) / 0.09m²
𝐹₃ = 9 x 10^9 N * 20ፀ² / 0.09m²
𝐹₃ = 20 x 10^9 N * 20ፀ² / 0.09m²
𝐹₃ ≈ 44,444,444 N
Now, we need to find the vector sum of these forces to determine the resultant force.
𝐹_resultant = √(𝐹₁² + 𝐹₂² + 𝐹₃²)
Substituting the calculated values:
𝐹_resultant = √((111,111,111 N)² + (177,777,778 N)² + (44,444,444 N)²)
𝐹_resultant ≈ √(12,345,679,012,346,567,432,098,134) N
Therefore, the resultant force on the charge 20ፀ due to Q1, Q2, and Q3 at a distance of 30cm is approximately equal to 3,511,881,424 N (rounded to the nearest whole number).