Calculate the resultant force at Q3
IF
Q1=-16 μC
distances from Q1 to Q2 is =0.6m
Q2=6 μC
distances from Q2 to Q3 is =0.3m
Q3=-8 μC
In simple steps
To calculate the resultant force at Q3, we need to calculate the forces between each pair of charges (Q1 and Q3, and Q2 and Q3) and add them vectorially.
First, let's calculate the force between Q1 and Q3.
Using Coulomb's Law, the formula to calculate the force between two charges is:
F = (k * |Q1| * |Q3|) / (distance^2)
Where:
- F is the force between the charges,
- k is the electrostatic constant (8.99 x 10^9 Nm^2/C^2),
- |Q1| and |Q3| are the magnitudes of the charges,
- distance is the distance between the charges.
Substituting in the values:
F1 = (8.99 x 10^9 Nm^2/C^2) * (16 μC) * (8 μC) / (0.6m)^2
Calculating this gives us F1 = 5.1584 N (taking the magnitudes of the charges into account).
Now, let's calculate the force between Q2 and Q3.
Using the same formula:
F2 = (8.99 x 10^9 Nm^2/C^2) * (6 μC) * (8 μC) / (0.3m)^2
Calculating this gives us F2 = 17.9584 N (taking the magnitudes of the charges into account).
Finally, we can calculate the resultant force at Q3 by adding the forces vectorially.
Resultant force F = F1 + F2
F = 5.1584 N + 17.9584 N
F = 23.1168 N
So, the resultant force at Q3 is 23.1168 N.
To calculate the resultant force at Q3, we need to find the individual forces between Q1 and Q3, and between Q2 and Q3. Then, we can sum up these forces.
Step 1: Calculate the force between Q1 and Q3 using Coulomb's law.
- Coulomb's law states that the force between two charged objects is given by: F = (k * |Q1 * Q3|) / r^2
- Here, k is the electrostatic constant (9 x 10^9 N * m^2 / C^2), Q1 is the charge of Q1 (-16 μC), Q3 is the charge of Q3 (-8 μC), and r is the distance between Q1 and Q3 (sum of the distances from Q1 to Q2 and from Q2 to Q3, which is 0.6m + 0.3m = 0.9m).
- Plugging in the values, we get:
F1-3 = (9 x 10^9 N * m^2 / C^2 * |-16 μC * -8 μC|) / (0.9m)^2
= (9 x 10^9 N * m^2 / C^2 * 128 μC^2) / 0.81m^2
= (9 x 128 x 10^9 N * m^2 / C^2) / 0.81m^2
= 1152 x 10^9 N / 0.81m^2
= 1422.22 x 10^9 N / m^2 (approximately)
Step 2: Calculate the force between Q2 and Q3 using Coulomb's law.
- Again, applying Coulomb's law, we get:
F2-3 = (k * |Q2 * Q3|) / r^2
= (9 x 10^9 N * m^2 / C^2 * |6 μC * -8 μC|) / (0.3m)^2
= (9 x 10^9 N * m^2 / C^2 * 48 μC^2) / 0.09m^2
= (9 x 48 x 10^9 N * m^2 / C^2) / 0.09m^2
= 432 x 10^9 N / 0.09m^2
= 4800 x 10^9 N / m^2 (approximately)
Step 3: Calculate the resultant force at Q3 by summing up the individual forces.
- Since both forces are acting in the same direction (Q1 and Q2 both attract Q3 due to having opposite charges), we can simply add them together.
Resultant Force at Q3 = F1-3 + F2-3
= 1422.22 x 10^9 N / m^2 + 4800 x 10^9 N / m^2
= 6222.22 x 10^9 N / m^2 (approximately)
Therefore, the resultant force at Q3 is approximately 6.22222 x 10^12 N/m^2.
To calculate the resultant force at point Q3, we need to calculate the individual forces between each pair of charges and then combine them vectorially.
1. Calculate the force between Q1 and Q2:
- Use Coulomb's Law: F = k * |Q1| * |Q2| / r^2
- k is the electrostatic constant, approximately 9 × 10^9 Nm^2/C^2
- |Q1| and |Q2| are the magnitudes of the charges
- r is the distance between the charges
- Plugging in the values:
F1,2 = (9 × 10^9 Nm^2/C^2) * (|-16 μC|) * (|6 μC|) / (0.6m)^2
2. Calculate the force between Q2 and Q3:
- Use Coulomb's Law again:
F2,3 = (9 × 10^9 Nm^2/C^2) * (|6 μC|) * (|-8 μC|) / (0.3m)^2
3. Calculate the net force at Q3:
- Since the forces are vectors, we need to pay attention to their directions.
- The force between Q1 and Q2 is repulsive (since they have opposite charges), so its direction is away from Q2.
- The force between Q2 and Q3 is attractive (since they have opposite charges), so its direction is towards Q2.
- Add the forces vectorially, taking their directions into account:
Resultant force at Q3 = F1,2 - F2,3
4. Calculate the magnitude and direction of the resultant force:
- Use the Pythagorean theorem to find the magnitude:
Magnitude of the resultant force = √[(F1,2 - F2,3)^2]
- To find the direction, use trigonometry (tangent):
Direction of the resultant force = arctan[(F1,2 - F2,3) / 0]
5. Substitute the values into the respective formulas and calculate the resultant force at Q3.