Three charges, each equal to +2.0 micro Columbus, are placed at three corner of a square 0.500 meter on a side, find the magnitude and direction of the net force on charge number 3.
add the three individual forces:you know each charge pair, and the distance.
To find the magnitude and direction of the net force on charge number 3, we can use Coulomb's Law. Coulomb's Law states that the magnitude of the electric 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 first calculate the force between charge number 3 and charge number 1. Since all three charges are equal, the magnitude of charge number 1 is also +2.0 microCoulombs. The distance between charge number 3 and charge number 1 is the length of the diagonal of the square, which is given by d = √(s^2 + s^2) = √(0.5^2 + 0.5^2) = √(0.25 + 0.25) = √0.5 = 0.7071 meters.
Using Coulomb's Law, the magnitude of the force between charge number 3 and charge number 1 is given by:
F₁₃ = k * (|q₁| * |q₃|) / d²,
where k is the electrostatic constant, |q₁| and |q₃| are the magnitudes of the charges, and d is the distance between them.
The magnitude of the charge is given as +2.0 microCoulombs, which is written as 2.0 * 10^(-6) Coulombs.
The electrostatic constant, k, is approximately equal to 9.0 * 10^9 N·m²/C².
Substituting the given values, we have:
F₁₃ = (9.0 * 10^9 N·m²/C²) * (2.0 * 10^(-6) C)^2 / (0.7071 m)^2.
Calculating this expression will give us the magnitude of the force between charge number 3 and charge number 1.
Next, we calculate the force between charge number 3 and charge number 2. The distance between them is the length of one side of the square, which is given as 0.500 meters.
Using Coulomb's Law in a similar fashion, we can determine the magnitude of the force between charge number 3 and charge number 2.
Once we have the magnitudes of these forces, we need to determine their direction. Since all the charges are positive, the forces will be repulsive.
To find the direction of the net force on charge number 3, we need to consider the vector sum of the two forces. If the forces are in the same direction, we add them together. If the forces are in opposite directions, we subtract them.
By considering the magnitudes and directions of the forces between charge number 3 and charges number 1 and 2, we can calculate the net force acting on charge number 3.