Force of attraction b/w two point charges placed at a separation ‘d’ in a medium is ‘F’. what would be the separation b/w them to have a force F/3. between the charges.

To determine the new separation between two point charges that results in a force of F/3, we can use Coulomb's law, which describes the force between two point charges. The law states that the force (F) between two charges (q1 and q2) separated by a distance (d) in a medium with a permittivity (ε) is given by the formula:

Coulomb's Law

The formula can be expressed as:

F = k * (|q1 * q2|) / (ε * d²)

Here, k is Coulomb's constant, |q1 * q2| is the absolute product of the magnitudes of the charges, ε is the permittivity of the medium, and d is the distance between the charges.

Initial Conditions

In your scenario, we know the initial force is F when the separation is d. Therefore, we can write:

F = k * (|q1 * q2|) / (ε * d²)

New Force Condition

Now, we want to find the new separation (let's call it d') such that the force becomes F/3. According to Coulomb's law, we can express this as:

F/3 = k * (|q1 * q2|) / (ε * (d')²)

Setting Up the Equation

We can set the two equations equal to each other, taking into account that the charges and the medium remain constant:

F/3 = (F * d²) / (d')²

Solving for d'

Now, we can rearrange this equation to solve for d':

• Multiply both sides by (d')²:
• F * d² = (F/3) * (d')²
• Divide both sides by (F/3):
• 3 * d² = (d')²

Taking the square root of both sides gives us:

d' = √(3) * d

Final Result

This means that to achieve a force of F/3 between the two charges, the new separation must be:

d' = √3 * d

In summary, by increasing the distance between the charges to √3 times the original distance, the force of attraction will reduce to one-third of its initial value. This relationship highlights how sensitive the electrostatic force is to changes in distance, illustrating the inverse square nature of the force as described by Coulomb's law.