Dielectric Constant Calculation - Interactive Physics Problem

Determining the Dielectric Constant

Two charges placed in air repel each other with a force of \(10^{-4}\,\text{N}\). When oil is introduced between the charges, the force drops to \(2.5 \times 10^{-5}\,\text{N}\). What is the dielectric constant of the oil?

Select the correct option:

• A) 2.5
• B) 0.25
• C) 2.0
• D) 4.0

Detailed Explanation

Coulomb's law in a vacuum (or air, approximately) is given by: \[ F = k \frac{q_1 q_2}{r^2}, \] where \( F \) is the force between the charges.

When a dielectric is introduced, the force is reduced by a factor equal to the dielectric constant \(\kappa\): \[ F' = \frac{F}{\kappa}. \]

Here, the force in air is: \[ F = 10^{-4}\,\text{N}, \] and the force in oil is: \[ F' = 2.5 \times 10^{-5}\,\text{N}. \]

Rearranging the equation to solve for \(\kappa\): \[ \kappa = \frac{F}{F'}. \]

Substitute the given values: \[ \kappa = \frac{10^{-4}}{2.5 \times 10^{-5}} = 4. \]

Hence, the dielectric constant of the oil is 4.0, which corresponds to option (D).