Question

Three equal charges are placed on the three corners of a square. If the force between q1 and q2 is F12 and that between q1 and q3 is F13, the ratio of magnitudes F12 ⁄ F13 is :

(a) √2
(b) 1/√2
(c) 2
(d) 1/2

Answer 1

The ratio of the magnitudes of the electrostatic forces F12 to F13 between equal charges placed on adjacent and diagonal corners of a square is 1/2, which corresponds to option (d).

Step-by-step explanation:

The question pertains to the electrostatic force between charges placed on the corners of a square. By Coulomb's law, the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Considering three equal charges at the corners of a square, F12 is the force between charges q1 and q2 situated at the adjacent corners of the square, and F13 is the force between charges q1 and q3 situated at the diagonal corners of the square. Since the diagonal of a square is √2 times the side, the distance between q1 and q3 is √2 times the distance between q1 and q2. Therefore, applying Coulomb's law and considering that the charges are equal, F12 / F13 will be (1/√2)², which simplifies to 1/2. Consequently, the ratio of the magnitudes F12 ⁄ F13 is 1/2, answering the student's question and indicating that option (d) is the correct choice.