Four charges are arranged in a square with sides of length 2.5cm. The two charges in the top right and bottom left corners are +3.0μC. The charges in the other two corners are -3.0μC. What is the net force exerted on the charge in the top right corner by the other three charges?
apply Coulomb's law to each charge and add them up.
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To calculate the net force exerted on the charge in the top right corner by the other three charges, we need to find the individual forces exerted by each charge and then add them up vectorially.
1. Calculate the distance between the charges:
The side length of the square is given as 2.5 cm. Since it is a square, the diagonals of the square will pass through the corners where the charges are located. Therefore, the distance between the charges is equal to the length of the diagonal, which can be calculated using the Pythagorean theorem.
Diagonal (d) = √(side length)^2 + (side length)^2
= √(2.5 cm)^2 + (2.5 cm)^2
= √(6.25 cm^2 + 6.25 cm^2)
= √(12.5 cm^2)
= √12.5 cm
= 3.536 cm (approximately)
2. Calculate the magnitude of each force:
The magnitude of the electrical 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 Coulomb's constant (9.0 x 10^9 N m^2/C^2), q1 and q2 are the charges, and d is the distance between the charges.
For the charges in the top right and bottom left corners:
F1 = (9.0 x 10^9 N m^2/C^2) * ((3.0 x 10^-6 C)^2) / (3.536 cm)^2
For the charges in the other two corners:
F2 = (9.0 x 10^9 N m^2/C^2) * ((3.0 x 10^-6 C) * (-3.0 x 10^-6 C)) / (3.536 cm)^2
3. Calculate the directions of the forces:
The direction of each force is along the line connecting the charges. Since the charges in the corners are diagonally opposite, the forces exerted by them will be along the diagonals.
The force from the charge in the top left corner will act in the bottom right direction, and the force from the charge in the bottom right corner will act in the top left direction.
4. Add up the forces vectorially:
To find the net force exerted on the charge in the top right corner, we need to subtract the force in the top left direction (F2) from the force in the bottom right direction (F1).
Net force = F1 - F2
Note: Since the forces are acting along diagonals, they have equal magnitudes, but opposite directions. So, the subtraction is simply like adding two vectors pointing in opposite directions.
5. Calculate the net force:
Substitute the values into the equation:
Net force = (F1) - (-F2)
= F1 + F2
Now you can calculate the net force by substituting the values of F1 and F2 into the equation.
To find the net force exerted on the charge in the top right corner by the other three charges, you can use Coulomb's Law. Coulomb's Law 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.
Step 1: Determine the distance between the charges
The square has sides of length 2.5 cm, so the distance between the charges in the top right and bottom left corners is equal to one of the sides of the square, which is 2.5 cm.
Step 2: Calculate the force between the charges
Using Coulomb's Law, the force between two charges can be calculated by the formula:
F = k * (q1 * q2) / r^2
where F is the force, k is the electrostatic constant (k = 9.0 x 10^9 Nm^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
In this case, the magnitudes of the charges are 3.0 μC and the distance between them is 2.5 cm (converted to meters: 0.025 m).
Since the charges in the other two corners are also 3.0 μC, we need to calculate the force between each charge pair and then find the vector sum of those forces.
Force between top right and bottom left corners:
F1 = k * (3.0 μC * 3.0 μC) / (0.025 m)^2
Step 3: Find the net force
Since the charges in the other two corners are also 3.0 μC, we need to calculate the force between each charge pair and then find the vector sum of those forces.
Force between top right and bottom right corners:
F2 = k * (3.0 μC * 3.0 μC) / (2.5 cm)^2
Force between top right and top left corners:
F3= k * (3.0 μC * 3.0 μC) / (2.5 cm)^2
Finally, to find the net force, add the individual forces vectorially. Since the charges in the bottom left and top right corners have the same magnitude, the forces between them will have equal magnitudes but opposite directions. The force between the charges in the top left and top right corners will have a different direction.
Net force = F1 - F2 - F3
Calculate the individual forces F1, F2, and F3, and then subtract F2 and F3 from F1. The resulting net force will give you the magnitude and direction of the force exerted on the charge in the top right corner by the other three charges.