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Three charges π‘ž1 = +2πœ‡πΆ π‘ž2 = βˆ’4πœ‡πΆ and q3=+5πœ‡C are placed on the vertices of an equilateral triangle of side 2.0 m.

1.1 Calculate the magnitude and direction of net electrostatic force acting on charge π‘ž1.

To calculate the net electrostatic force acting on charge π‘ž1, we need to find the forces between π‘ž1 and π‘ž2, and between π‘ž1 and π‘ž3. The force between two charges can be calculated using Coulomb's Law:

𝐹 = π‘˜ * (π‘ž1 * π‘ž2) / π‘Ÿ^2

Where:
- 𝐹 is the force between the charges
- π‘˜ is Coulomb's constant (9.0 x 10^9 Nm^2/C^2)
- π‘ž1 and π‘ž2 are the magnitudes of the charges
- π‘Ÿ is the distance between the charges

Let's calculate the force between π‘ž1 and π‘ž2 first. Since the triangle is equilateral, the distance between them is equal to the side length of the triangle, which is 2.0 m.
𝐹12 = (9.0 x 10^9 Nm^2/C^2) * ((2 μC * -4 μC) / (2.0 m)^2)

Simplifying this expression:
𝐹12 = (9.0 x 10^9 Nm^2/C^2) * (-8 πœ‡C^2) / 4.0 m^2

𝐹12 = -18πœ‡N (Note that the direction is attractive, since the charges are opposite in sign)

Now let's calculate the force between π‘ž1 and π‘ž3. Again, the distance between them is 2.0 m.
𝐹13 = (9.0 x 10^9 Nm^2/C^2) * ((2 μC * 5 μC) / (2.0 m)^2)

Simplifying this expression:
𝐹13 = (9.0 x 10^9 Nm^2/C^2) * (10 πœ‡C^2) / 4.0 m^2

𝐹13 = 45πœ‡N (The direction is repulsive, since the charges are the same in sign)

To find the net force on π‘ž1, we need to find the vector sum of 𝐹12 and 𝐹13. Since they are along the same line, we can simply add their magnitudes.
𝐹net = |𝐹12| + |𝐹13|

𝐹net = |-18πœ‡N| + |45πœ‡N|

𝐹net = 63πœ‡N

Therefore, the magnitude of the net electrostatic force acting on charge π‘ž1 is 63 πœ‡N, and the direction is towards π‘ž3.

To calculate the magnitude and direction of the net electrostatic force acting on charge q1, we can use the principle of superposition. According to this principle, the net force on a charge due to multiple charges is the vector sum of the individual forces between the charges.

Step 1: Calculate the force between q1 and q2:
The magnitude of the force between two charges, q1 and q2, is given by Coulomb's Law:

F12 = (k * |q1 * q2|) / r12^2

where:
- F12 is the force between q1 and q2,
- k is the electrostatic constant (9 * 10^9 Nm^2/C^2),
- q1 and q2 are the magnitudes of the charges, and
- r12 is the distance between q1 and q2.

In this case, q1 = +2ΞΌC, q2 = -4ΞΌC, and the distance between them is 2.0m (as they are placed on the vertices of an equilateral triangle with a side length of 2.0m). Plugging these values into the equation, we can calculate F12.

F12 = (9 * 10^9 * |2 * 10^-6 * (-4 * 10^-6)|) / (2.0^2)
= 72 * 10^-5 N

Step 2: Calculate the force between q1 and q3:
Similarly, we can calculate the force between q1 and q3 using Coulomb's Law. Since q1 and q3 have the same magnitude (+2ΞΌC and +5ΞΌC), the force between them will have the same magnitude as F12.

F13 = F12 = 72 * 10^-5 N

Step 3: Calculate the net force on q1:
Since q1 experiences forces in opposite directions (due to q2 and q3), we need to consider the vector sum of these forces. In other words, we need to add the forces F12 and F13 as vectors.

To do this, we can draw a vector triangle with F12 and F13 as the sides. Since both forces have the same magnitude and opposite directions, they cancel each other out, resulting in a net force of zero.

Therefore, the magnitude of the net electrostatic force acting on charge q1 is zero, and its direction is undefined (since there is no net force).

Note that if the magnitudes of the charges q1, q2, and q3 were different, or if the distances between the charges were not equal, the net force acting on q1 would not be zero, and we would need to calculate it accordingly.

To calculate the magnitude and direction of the net electrostatic force acting on charge q1, we need to consider the individual electrostatic forces between q1 and q2, q1 and q3, and the resultant force from these two forces.

Step 1: Calculate the force between q1 and q2 using Coulomb's Law:
The electrostatic force (F) between two charges can be calculated using the formula:
F = (k * q1 * q2) / r^2

where k is the electrostatic constant (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.

Given:
q1 = +2 ΞΌC = 2 x 10^-6 C (charge of q1)
q2 = -4 ΞΌC = -4 x 10^-6 C (charge of q2)
r = side length of the equilateral triangle = 2 m

Plugging in the values:
F1-2 = (9 x 10^9 Nm^2/C^2) * (2 x 10^-6 C) * (-4 x 10^-6 C) / (2 m)^2

Step 2: Calculate the force between q1 and q3 using Coulomb's Law:
Given:
q3 = +5 ΞΌC = 5 x 10^-6 C (charge of q3)

Using the same formula as before:
F1-3 = (9 x 10^9 Nm^2/C^2) * (2 x 10^-6 C) * (5 x 10^-6 C) / (2 m)^2

Step 3: Calculate the net force:
To find the net force acting on q1, we need to sum up the forces F1-2 and F1-3. Since these forces have different directions, we need to consider their vector nature.

Net force = F1-2 + F1-3

Step 4: Determine the magnitude and direction of the net force:
Calculate the magnitude:
Magnitude of the net force = |Net force|

Calculate the direction:
The direction of the net force can be determined by finding the angle between the net force vector and the positive x-axis.

So, using the calculated values, you can substitute them into the equations to find the magnitude and direction of the net electrostatic force acting on charge q1.