Four equal point charges each 16 microcoulomb are placed on the four corners of square of side 0.2m.Calculate the force on any one of the charge.
To calculate the force on any one of the charges, we can use Coulomb's Law.
Coulomb's Law states that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (q1 * q2) / r^2
Where:
F is the force between the charges,
k is the Coulomb's constant (8.99 * 10^9 Nm^2/C^2),
q1 and q2 are the charges, and
r is the distance between the charges.
The distance between any two charges in the square is the length of the side of the square.
Let's calculate the force on any one of the charges:
1. Calculate the distance between two charges:
The side length of the square is given as 0.2 m, which is the same as the distance between any two charges.
2. Calculate the force using Coulomb's Law:
F = k * (q1 * q2) / r^2
Substituting the values:
F = (8.99 * 10^9 Nm^2/C^2) * (16 μC * 16 μC) / (0.2 m)^2
Calculating the force will give you the final answer.
To calculate the force on any one of the charges, we can use Coulomb's law. Coulomb's law states that the force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
The formula for Coulomb's law is:
F = (k * |q1 * q2|) / r^2
Where:
F is the force between the charges,
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.
In this case, we need to calculate the force on one of the charges due to the other three charges. Since all the charges are equal, we can assume that the charges at the corners of the square are the same and the distances between them are equal.
Let's assume that we want to calculate the force on one charge at a corner due to the other three charges. The distance between any two adjacent corners of the square can be calculated using Pythagoras' theorem since it is a right-angled triangle.
Using Pythagoras' theorem:
a^2 + b^2 = c^2
Here, a = b = 0.2m (side length of the square)
So, c^2 = (0.2)^2 + (0.2)^2
= 0.04 + 0.04
= 0.08
Therefore, c = sqrt(0.08) = 0.2828m (approx.)
Now that we have the distance, we can calculate the force using Coulomb's law:
F = (k * |q1 * q2|) / r^2
F = (9 x 10^9 Nm^2/C^2 * (16 x 10^-6 C)^2) / (0.2828m)^2
F = (9 x 10^9 * 256 x 10^-12) / 0.08
F = 2.88 x 10^-5 N
So, the force on any one of the charges is approximately 2.88 x 10^-5 Newtons.