Three equal charges each +Q, placed at the corners of on equilateral triangle of side 'a' what will be the force on any charge

The force on any charge in an equilateral triangle with equal charges at each corner can be calculated using Coulomb's Law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Step 1: Identify the charges and the distance between them. In this case, each charge is +Q and the distance between each charge (the length of the sides of the equilateral triangle) is 'a'.

Step 2: Calculate the force between two charges using Coulomb's Law. The formula is F = kQ1Q2/r^2, where k is Coulomb's constant (approximately 9.0 x 10^9 N m^2/C^2), Q1 and Q2 are the charges, and r is the distance between them. In this case, F = kQQ/a^2.

Step 3: Since the force between two charges acts along the line joining the charges, the net force on any charge will be the vector sum of the forces due to the other two charges. In an equilateral triangle, these two forces are equal in magnitude and at an angle of 120 degrees to each other.

Step 4: The net force can be calculated using the formula F_net = sqrt(F1^2 + F2^2 + 2F1F2*cos120), where F1 and F2 are the forces on the charge due to the other two charges. Since F1 = F2 = F, this simplifies to F_net = sqrt(3)*F.

Step 5: Substitute the value of F from step 2 into the equation from step 4 to get the final answer. F_net = sqrt(3)kQ^2/a^2.