To calculate the magnitude and direction of the forces acting on one of the charges in the equilateral triangle, we can use the principle of superposition and Coulomb's Law.
First, let's consider one of the charges at a corner of the equilateral triangle. Due to the symmetry of the triangle, the forces acting on this charge will be exactly the same in magnitude but opposite in direction along the sides of the triangle.
The magnitude of the force between two charges is given by Coulomb's Law:
F = k * |q1 * q2| / r^2
Where:
F is the magnitude of the force
k is Coulomb's constant (8.99 x 10^9 N m^2/C^2)
q1 and q2 are the charges (8uc = 8 x 10^-6 C in this case)
r is the distance between the charges (in this case, the length of the side of the equilateral triangle, 2m)
Let's consider the charge at the bottom-left corner. The force on this charge due to the charge at the bottom-right corner can be calculated as:
F = k * |q1 * q2| / r^2
F = 8.99 * 10^9 * |8 * 10^-6 * 8 * 10^-6| / 2^2
F = 8.99 * 10^9 * 64 * 10^-12 / 4
F = 8.99 * 10^9 * 16 * 10^-12
F = 143.84 * 10^-3
F = 0.14384 N
Therefore, the magnitude of the force acting on one of the charges at the corner of the equilateral triangle is 0.14384 N. This force will be directed along the sides of the equilateral triangle, towards the other charges at the corners.
Equal charges of 8uc are placed of the three corners of an equilateral triangle 2m on a side calculated the magnitude and direction of the the forces on ones of the charges
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