Calculation of Force on Each Charge in an Equilateral Triangle

Given:
- Three identical point charges of Q coulomb each
- Placed at the vertices of an equilateral triangle
- Distance between the charges is 10 cm

To Find:
- Magnitude of the force on each charge

Solution:

1. Charge Distribution

The given problem involves three charges, each of Q coulomb, placed at the vertices of an equilateral triangle. Since the charges are identical, we can assume that they are placed at the same distance from each other.

2. Calculation of Electric Field

Using the principle of superposition, we can calculate the electric field at any point in space due to these charges. Let us consider a point P at a distance r from one of the charges.

The electric field at point P due to one of the charges is given by:

E = kQ/r^2

Where k is the Coulomb's constant, Q is the charge and r is the distance between the charge and point P.

Since there are three charges, the total electric field at point P will be the vector sum of the electric fields due to each charge.

3. Calculation of Force

Using the electric field, we can calculate the force on each charge. The force on a charge q in an electric field E is given by:

F = qE

Since the charges are identical, each charge experiences the same force. Hence, the magnitude of the force on each charge is given by:

F = QE

Substituting the value of E from step 2, we get:

F = kQ^2/r^2

4. Calculation of Distance

In an equilateral triangle, the distance between two charges is given by:

d = (√3)/2 * a

Where a is the length of the side of the triangle. In this case, the distance between the charges is given as 10 cm. Hence, we can calculate the length of the side of the equilateral triangle as:

a = 20/√3 cm

5. Calculation of Force Magnitude

Substituting the value of r as the distance between the charges, and Q as the charge on each charge, we get:

F = (9 × 10^9) * Q^2/(10/√3)^2

F = 3√3 * 10^-2 * Q^2 N

Hence, the magnitude of the force on each charge is 3√3 * 10^-2 * Q^2 N.

Conclusion:

In this problem, we calculated the magnitude of the force on each charge in an equilateral triangle. We used the principles of superposition and Coulomb's law to calculate the electric field and force on each charge. The distance between the charges was calculated using the formula for an equilateral triangle. The final answer was expressed in terms of Q, the charge on each charge.