Question

A force of 80 newton acts between two point charges placed in air at a fixed distance. When the same charges are placed at the same distance in a dielectric medium, the force becomes 8 newton. The dielectric constant of the medium is:

• A. 10
• B. zero
• C. 0.1
• D. 8

Hint:

In a medium the Coulomb force drops by the factor of the dielectric constant, so \( K = F_{air}/F_{medium} \).

Answer 1

The Correct Option is A

Step 1: Recall how a dielectric changes force.
Placing a dielectric of constant \(K\) between two charges reduces the electrostatic force by the factor \(K\). In symbols, if \(F_0\) is the force in vacuum/air, then in the medium \(F = F_0/K\).

Step 2: Insert the numbers directly.
We are told \(F_0 = 80\) N (air) and \(F = 8\) N (medium). Therefore \(8 = 80/K\).

Step 3: Solve for \(K\).
Rearranging, \(K = 80/8\).

Step 4: Evaluate.
\(K = 10\), a pure number (dielectric constant is dimensionless).

Step 5: Sanity check.
The medium made the force ten times smaller, which is exactly what a dielectric constant of 10 should do. This confirms the first choice.
\[\boxed{K = 10}\]