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 Q2 is =0.3m
Q3=-8 μC
To calculate the resultant force at Q3, we need to calculate the individual forces between Q1 and Q3 and between Q2 and Q3.
The formula to calculate the force between two charged particles is:
F = k * (|Q1| * |Q2|) / r^2
where F is the force, k is the Coulomb's constant (k = 8.99 * 10^9 Nm^2/C^2), Q1 and Q2 are the charges in Coulombs, and r is the distance in meters.
First, let's calculate the force between Q1 and Q3:
|Q1| = |-16 μC| = 16 μC
r1 = 0.6m
F1 = k * (|Q1| * |Q3|) / r1^2
= (8.99 * 10^9 Nm^2/C^2) * ((16 * 10^-6 C) * (8 * 10^-6 C)) / (0.6m)^2
Next, calculate the force between Q2 and Q3:
|Q2| = |6 μC| = 6 μC
r2 = 0.3m
F2 = k * (|Q2| * |Q3|) / r2^2
= (8.99 * 10^9 Nm^2/C^2) * ((6 * 10^-6 C) * (8 * 10^-6 C)) / (0.3m)^2
Finally, we can find the resultant force at Q3 by summing up F1 and F2 using vector addition:
resultant force = √((F1^2 + F2^2) + 2 * F1 * F2 * cosθ)
where θ is the angle between the forces F1 and F2.
Since the problem does not provide the angle between the forces, we cannot calculate the resultant force without this information.
To calculate the resultant force at Q3, we need to consider the forces exerted by Q1 and Q2 on Q3. The formula to calculate the electrostatic force between two charges is given by Coulomb's Law:
F = k * (|Q1| * |Q2|) / r²
Where:
- F is the electrostatic force,
- k is the electrostatic constant (9 × 10^9 N m²/C²),
- |Q1| and |Q2| are the magnitudes of the charges, and
- r is the distance between the charges.
Let's calculate the forces exerted by Q1 and Q2 on Q3 separately and then combine them to find the resultant force.
1. Force exerted by Q1 on Q3:
Given:
Q1 = -16 μC
Q3 = -8 μC
Distance from Q1 to Q3 (r1) = 0.6 m
Using Coulomb's Law:
F1 = (k * |Q1| * |Q3|) / r1²
Substituting the values:
F1 = (9 × 10^9 N m²/C² * 16 μC * 8 μC) / (0.6 m)²
Calculating the result:
F1 = (9 × 10^9 * 16 * 8) / (0.6)² N
2. Force exerted by Q2 on Q3:
Given:
Q2 = 6 μC
Q3 = -8 μC
Distance from Q2 to Q3 (r2) = 0.3 m
Using Coulomb's Law:
F2 = (k * |Q2| * |Q3|) / r2²
Substituting the values:
F2 = (9 × 10^9 N m²/C² * 6 μC * 8 μC) / (0.3 m)²
Calculating the result:
F2 = (9 × 10^9 * 6 * 8) / (0.3)² N
3. Combining the forces:
To find the resultant force at Q3, we need to consider the directions of the forces. Since Q1 and Q3 are of the same charge sign, their forces will repel each other. On the other hand, Q2 and Q3 are of opposite charge signs, so their forces will attract each other. Thus, we need to subtract the force exerted by Q1 from the force exerted by Q2 to get the net force:
Resultant force at Q3 = F2 - F1
Substituting the respective values:
Resultant force at Q3 = [(9 × 10^9 * 6 * 8) / (0.3)²] - [(9 × 10^9 * 16 * 8) / (0.6)²] N
Calculating the result will give you the resultant force at Q3.
To calculate the resultant force at point Q3, we need to take into account the forces exerted by both Q1 and Q2 on Q3. The force between two charged objects can be calculated using Coulomb's law:
F = k * |Q1 * Q2| / r^2
where:
F is the force between the charges,
k is the electrostatic constant (9 × 10^9 Nm^2/C^2),
Q1 and Q2 are the magnitudes of the charges,
and r is the distance between the charges.
Let's first calculate the force exerted by Q1 on Q3. Given:
Q1 = -16 μC
Distance from Q1 to Q3 = 0.6 m
We can plug these values into the Coulomb's law formula:
F1 = (9 × 10^9 Nm^2/C^2) * |-16 μC| * |-8 μC| / (0.6 m)^2
Next, let's calculate the force exerted by Q2 on Q3. Given:
Q2 = 6 μC
Distance from Q2 to Q3 = 0.3 m
We plug the values into the Coulomb's law formula:
F2 = (9 × 10^9 Nm^2/C^2) * |-6 μC| * |-8 μC| / (0.3 m)^2
Now, we can calculate the resultant force at Q3 by taking the vector sum of the forces F1 and F2:
Resultant Force at Q3 = F1 + F2
Simply add the magnitudes of F1 and F2 to find the resultant force. If the charges have opposite signs, the forces will be in opposite directions. If the charges have the same sign, the forces will be in the same direction. The final result will give the magnitude and direction of the resultant force at Q3.