Three point charges have equal magnitudes, two being positive and one negative. These charges are fixed to the corners of an equilateral triangle. The magnitude of each of the charges is 3.66 μC, and the lengths of the sides of a triangle are 2.15 cm. Calculate the magnitude of the net force that each charge experiences. Input A's net force first and C's net force last.
To calculate the magnitude of the net force that each charge experiences, we can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Let's start by calculating the distance between each charge and the other charges.
Since the charges are fixed to the corners of an equilateral triangle, the distance between any two charges is equal to the length of the side of the triangle.
Given that the length of the sides of the triangle is 2.15 cm, we can now proceed to calculate the net force for each charge.
First, let's calculate the net force on charge A, which is positive.
To calculate the net force on charge A, we need to consider the forces exerted by the other two charges.
The force between two charges can be determined using Coulomb's Law formula:
F = k * (|q1| * |q2|) / r^2
Where:
- F is the force between the charges
- k is Coulomb's constant, approximately equal to 9 × 10^9 N m^2 / C^2
- |q1| and |q2| are the magnitudes of the charges
- r is the distance between the charges
In our case, the magnitudes of the charges are 3.66 μC = 3.66 × 10^-6 C, and the distance between the charges is 2.15 cm = 2.15 × 10^-2 m.
Plugging these values into the formula, we get:
F = (9 × 10^9 N m^2 / C^2) * ((3.66 × 10^-6 C) * (3.66 × 10^-6 C)) / ((2.15 × 10^-2 m)^2)
Calculating this expression will give us the magnitude of the net force experienced by charge A.
Now for charge C, which is also positive, we need to consider the forces exerted by the other two charges. Since it is an equilateral triangle, the magnitudes and distances will be the same as those for charge A.
Using the same formula, we can calculate the net force on charge C:
F = (9 × 10^9 N m^2 / C^2) * ((3.66 × 10^-6 C) * (3.66 × 10^-6 C)) / ((2.15 × 10^-2 m)^2)
Finally, the net force on charge B, which is negative, can be calculated by considering the forces exerted by the other two charges. However, the sign of the force will be opposite.
F = -(9 × 10^9 N m^2 / C^2) * ((3.66 × 10^-6 C) * (3.66 × 10^-6 C)) / ((2.15 × 10^-2 m)^2)
Calculating these expressions will give us the magnitudes of the net forces experienced by charges A, B, and C.