Three positive point charges of 3.0 nC, 6.0 nC, and 2.0 nC, respectively, are arranged
in a triangular pattern, as shown below. Find the magnitude and direction of the electric
force acting on the 6.0 nC charge.
what is the answer of the question
To find the magnitude and direction of the electric force acting on the 6.0 nC charge, we can use Coulomb's Law. Coulomb's Law states that the electric force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
1. First, let's label the charges and their magnitudes:
Q1 = 3.0 nC
Q2 = 6.0 nC (this is the charge we are interested in)
Q3 = 2.0 nC
2. Next, let's determine the distances between the charges. In this case, since they are arranged in a triangular pattern, we need to determine the distances between Q2 and Q1, Q2 and Q3, and Q1 and Q3. The diagram is needed for this step.
3. Once we have the distances between the charges, we can use Coulomb's Law to calculate the force between Q2 and each of the other charges. The formula for Coulomb's Law is:
F = k * |Q1| * |Q2| / r^2
where F is the magnitude of the electric force, k is the electrostatic constant (approximately 9 x 10^9 Nm^2/C^2), |Q1| and |Q2| are the magnitudes of the charges, and r is the distance between the charges.
4. Lastly, we can find the net electric force on Q2 by vector addition. Since the charges are arranged in a triangular pattern, the net force can be found by summing up the individual forces using vector addition.
Once you have all the necessary values and perform the calculations, you will obtain the magnitude and direction of the electric force acting on the 6.0 nC charge.
To find the magnitude and direction of the electric force acting on the 6.0 nC charge, we can use Coulomb's Law.
Coulomb's Law states that the magnitude of the electric force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's label the charges: The 3.0 nC charge as Q1, the 6.0 nC charge as Q2, and the 2.0 nC charge as Q3.
Step 1: Calculate the magnitude of the electric force between Q1 and Q2.
The formula for the electric force is F = (k * |Q1| * |Q2|) / r^2
Where:
F is the magnitude of the electric force
k is Coulomb's constant (k ≈ 8.99 * 10^9 N*m^2/C^2)
|Q1| and |Q2| are the magnitudes of the charges
r is the distance between the charges
In this case, the distance between Q1 and Q2 is the length of one side of the equilateral triangle formed by the three charges. Let's label this distance as "s".
Using Q1 = 3.0 nC, Q2 = 6.0 nC, and r = s, we have:
F12 = (8.99 * 10^9 N*m^2/C^2) * (3.0 * 10^-9 C) * (6.0 * 10^-9 C) / s^2
Step 2: Calculate the magnitude of the electric force between Q2 and Q3.
Using the same formula as above, we have:
F23 = (8.99 * 10^9 N*m^2/C^2) * (6.0 * 10^-9 C) * (2.0 * 10^-9 C) / s^2
Step 3: Calculate the magnitude of the electric force between Q1 and Q3.
Using the same formula as above, we have:
F13 = (8.99 * 10^9 N*m^2/C^2) * (3.0 * 10^-9 C) * (2.0 * 10^-9 C) / s^2
Step 4: Add up the forces.
The total electric force on Q2 is the vector sum of the three forces:
Fnet = F12 + F23 + F13
Step 5: Calculate the magnitude and direction of the net force.
Finally, we can calculate the magnitude and direction of the net electric force acting on Q2 by calculating the magnitude and direction of Fnet.
To find the direction of Fnet, we consider the vector nature of forces. Since all three forces are in different directions, we need to add them using vector addition. The direction of Fnet will be the direction of this resultant vector.
To find the magnitude of Fnet, we add the magnitudes of the three forces.
Note: Since the diagram of the arrangement of charges was not provided, we assume that the charges form an equilateral triangle.
Please provide the length of the side of the triangle (s), and I'll calculate the magnitude and direction of the net electric force acting on the 6.0 nC charge.