Question

Three equal charges (\( q \)) are placed at corners of an equilateral triangle of side \( a \). The force on any charge is –

• A. zero
• B. \( \sqrt{3} \frac{Kq^2}{a^2} \)
• C. \( \frac{Kq^2}{\sqrt{3} a^2} \)
• D. \( 3 \sqrt{3} \frac{Kq^2}{a^2} \)

Hint:

In an equilateral triangle, the resultant force on any charge can be calculated by vector addition of the forces from the other two charges.

Answer 1

The Correct Option is B

Step 1: Analyze the forces between charges.
The force between each pair of charges is given by Coulomb's law: \[ F = \frac{kq^2}{a^2} \] Since the charges are at the corners of an equilateral triangle, the net force on each charge is the vector sum of the forces due to the other two charges.
Step 2: Calculate the resultant force.
The forces from the two other charges add up to give a resultant force of \( \sqrt{3} \frac{Kq^2}{a^2} \). Final Answer: \[ \boxed{\sqrt{3} \frac{Kq^2}{a^2}} \]