Calculate the resultant force at Q3
IF
Q1=-16 μC
distances from Q1 to Q2 is =0.6m
Q2=6 μC
distances from Q1 to Q3 is =0.3m
Q3=-8 μC
In simple steps
To calculate the resultant force at Q3, we need to consider the forces from Q1 and Q2 acting on Q3.
The force between Q1 and Q3 can be calculated using Coulomb's law:
F1 = (k * |Q1 * Q3|) / r1^2
Where k is the electrostatic constant (9 * 10^9 Nm^2/C^2), Q1 and Q3 are the charges (-16 μC and -8 μC respectively), and r1 is the distance between Q1 and Q3 (0.3m).
Substituting the values:
F1 = (9 * 10^9 * |-16 * -8|) / 0.3^2
F1 = (9 * 10^9 * 128) / 0.09
F1 ≈ 1.536 * 10^13 N
The force between Q2 and Q3 can also be calculated using Coulomb's law:
F2 = (k * |Q2 * Q3|) / r2^2
Where Q2 is the charge (6 μC), and r2 is the distance between Q2 and Q3 (0.6m).
Substituting the values:
F2 = (9 * 10^9 * |6 * -8|) / 0.6^2
F2 = (9 * 10^9 * 48) / 0.36
F2 ≈ 1.2 * 10^11 N
To find the resultant force at Q3, we need to calculate the vector sum of F1 and F2:
Resultant force = F1 + F2
Resultant force ≈ 1.536 * 10^13 N + 1.2 * 10^11 N
Resultant force ≈ 1.548 * 10^13 N
Therefore, the resultant force at Q3 is approximately 1.548 * 10^13 N.
To calculate the resultant force at Q3, we need to find the individual forces between each pair of charges and then add them up. Here are the steps to calculate the resultant force at Q3:
Step 1: Calculate the force between Q1 and Q2.
The formula to calculate the force between two charges is given by Coulomb's law:
F₁₂ = (k * |Q1 * Q2|) / r₁₂²
where F₁₂ is the force between Q1 and Q2, k is Coulomb's constant (8.99 x 10⁹ Nm²/C²), Q1 and Q2 are the magnitudes of the charges, and r₁₂ is the distance between the charges.
Substituting the given values:
Q1 = -16 μC (-16 x 10^-6 C)
Q2 = 6 μC (6 x 10^-6 C)
r₁₂ = 0.6 m
Calculating the force F₁₂:
F₁₂ = (8.99 x 10⁹ Nm²/C² * |-16 x 10^-6 C * 6 x 10^-6 C|) / (0.6 m)²
F₁₂ = (8.99 x 10⁹ Nm²/C² * 96 x 10^-12 C²) / 0.36 m²
F₁₂ = (8.99 x 10⁹ Nm² * 96 x 10^-12 C²) / 0.36 m²
F₁₂ = 2.40 x 10⁻³ N
Step 2: Calculate the force between Q1 and Q3.
Using the same formula, we can calculate the force between Q1 and Q3.
Q1 = -16 μC (-16 x 10^-6 C)
Q3 = -8 μC (-8 x 10^-6 C)
r₁₃ = 0.3 m
Calculating the force F₁₃:
F₁₃ = (8.99 x 10⁹ Nm²/C² * |-16 x 10^-6 C * -8 x 10^-6 C|) / (0.3 m)²
F₁₃ = (8.99 x 10⁹ Nm²/C² * 128 x 10^-12 C²) / 0.09 m²
F₁₃ = (8.99 x 10⁹ Nm² * 128 x 10^-12 C²) / 0.09 m²
F₁₃ = 1.6031 x 10⁻² N
Step 3: Calculate the net force at Q3.
Since the forces between Q1 and Q2 and between Q1 and Q3 act in opposite directions due to opposite charges, we need to subtract the force F₁₂ from F₁₃ to get the net force at Q3.
Net Force at Q3 = F₁₃ - F₁₂
Net Force at Q3 = 1.6031 x 10⁻² N - 2.40 x 10⁻³ N
Net Force at Q3 = 1.359 x 10⁻² N
Therefore, the resultant force at Q3 is 1.359 x 10⁻² N.
To calculate the resultant force at Q3, we need to consider the forces between Q3 and Q1 and between Q3 and Q2. Let's break it down into simple steps:
Step 1: Calculate the force between Q3 and Q1.
To calculate the force, we will use Coulomb's Law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * ((Q1 * Q3) / r^2)
Where:
F is the force between Q3 and Q1
k is the electrostatic constant (k = 9 * 10^9 Nm^2/C^2)
Q1 and Q3 are the charges of Q1 and Q3, respectively
r is the distance between Q1 and Q3
Plugging in the values:
Q1 = -16 μC
Q3 = -8 μC
r = 0.3m
F1 = (9 * 10^9) * ((-16 * 10^-6) * (-8 * 10^-6)) / (0.3^2)
Step 2: Calculate the force between Q3 and Q2.
Using the same formula as in Step 1, but with different values:
Q2 = 6 μC
r = 0.6m
F2 = (9 * 10^9) * ((-8 * 10^-6) * (6 * 10^-6)) / (0.6^2)
Step 3: Calculate the resultant force.
Since forces are vector quantities, we need to consider their directions. The force between Q1 and Q3 is attractive, and the force between Q2 and Q3 is repulsive. So, we need to subtract the force F2 from F1.
Resultant Force = F1 - F2
Substituting the values and calculating the resultant force:
Resultant Force = F1 - F2
Step 4: Calculate the final value.
Perform the calculation to find the resultant force.
Finally, plug in the values and evaluate the equation to find the resultant force at Q3.