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
IN SIMPLE STEPS
To calculate the resultant force at Q3, we need to consider the forces from Q1 and Q2 on Q3. The force between two charges can be calculated using Coulomb's law:
F = k * (Q1 * Q2) / d^2
where F is the force, k is the electrostatic constant (9 x 10^9 N*m^2/C^2), Q1 and Q2 are the charges, and d is the distance between the charges.
First, let's calculate the force from Q1 on Q3:
F1 = k * (Q1 * Q3) / d1^2
Given Q1 = -16 μC, Q3 = -8 μC, and d1 = 0.6m:
F1 = (9 x 10^9 N*m^2/C^2) * (-16 μC * -8 μC) / (0.6m)^2
F1 = (9 x 10^9 N*m^2/C^2) * (128 x 10^-12 C^2) / (0.36m^2)
F1 = (9 x 10^9 N*m^2/C^2) * (1.28 x 10^-10) / 0.1296
F1 = 88.8889 N
Next, let's calculate the force from Q2 on Q3:
F2 = k * (Q2 * Q3) / d2^2
Given Q2 = 6 μC, Q3 = -8 μC, and d2 = 0.3m:
F2 = (9 x 10^9 N*m^2/C^2) * (6 μC * -8 μC) / (0.3m)^2
F2 = (9 x 10^9 N*m^2/C^2) * (-48 x 10^-12 C^2) / (0.09m^2)
F2 = (9 x 10^9 N*m^2/C^2) * (-4.8 x 10^-10) / 0.0081
F2 = -400000 N
Now, to find the resultant force at Q3, we need to add the forces F1 and F2:
Resultant force (FR) = F1 + F2
FR = 88.8889 N + (-400000 N)
FR = -399911.1111 N
Therefore, the resultant force at Q3 is approximately -399911.1111 N.
To calculate the resultant force at Q3, we need to consider the forces between Q1 and Q3, as well as Q2 and Q3. The formula to calculate the force between two charged particles is given by Coulomb's law:
F = (k * |Q1 * Q2|) / r^2
where F is the force, k is the electrostatic constant (k = 9 × 10^9 Nm^2/C^2), |Q1 * Q2| is the magnitude of the product of the charges, and r is the distance between the charges.
Let's calculate the force between Q1 and Q3 first:
F1 = (9 × 10^9 * |(-16 μC) * (-8 μC)|) / (0.3)^2
Simplifying:
F1 = (9 × 10^9 * 128 μC^2) / 0.09
F1 = 1.28 × 10^10 N
Next, let's calculate the force between Q2 and Q3:
F2 = (9 × 10^9 * |(6 μC) * (-8 μC)|) / (0.6)^2
Simplifying:
F2 = (9 × 10^9 * 48 μC^2) / 0.36
F2 = 1.2 × 10^10 N
Finally, to calculate the resultant force at Q3, we need to add the forces:
Resultant Force at Q3 = F1 + F2
Resultant Force at Q3 = 1.28 × 10^10 N + 1.2 × 10^10 N
Resultant Force at Q3 = 2.48 × 10^10 N
Therefore, the resultant force at Q3 is 2.48 × 10^10 N.
To calculate the resultant force at Q3, we need to calculate the individual forces between Q1 and Q3, and Q2 and Q3, and then find the vector sum of these forces.
Step 1: Calculate the force between Q1 and Q3
The force between two charges can be calculated using Coulomb's Law:
Force = (k * |Q1| * |Q3|) / (distance^2)
where k is the electrostatic constant (9 x 10^9 Nm^2/C^2), |Q1| and |Q3| are the magnitudes of the charges, and distance is the separation distance between the charges.
Given:
|Q1| = 16 μC (microcoulombs)
|Q3| = 8 μC (microcoulombs)
distance = 0.6 m
Substituting the values into the formula:
Force1 = (9 x 10^9 Nm^2/C^2 * 16 μC * 8 μC) / (0.6m^2)
Step 2: Calculate the force between Q2 and Q3
Using the same formula, we can calculate the force between Q2 and Q3.
Given:
|Q2| = 6 μC (microcoulombs)
distance = 0.3 m
Force2 = (9 x 10^9 Nm^2/C^2 * 6 μC * 8 μC) / (0.3m^2)
Step 3: Find the vector sum of the forces
To find the resultant force at Q3, we need to add the forces calculated in step 1 and step 2, taking into account their directions.
To find the direction, we need to consider the sign of the charge. Like charges repel each other, so the forces between Q1 and Q3 and Q2 and Q3 will be in the opposite direction.
Since the charges involved are negative, the forces will be attractive forces.
The resultant force can be calculated using vector addition:
Resultant force = Force1 - Force2
Now substitute the values for Force1 and Force2 and perform the calculation.
This will give you the magnitude and direction of the resultant force at Q3.