Question

Two point charges placed in air separated by distance \(R\) exert a force \(F\) on each other. Now the space between those charges is filled with dielectric constant \(K\). At distance \(R_1\) between the charges, the same force is exerted as \(F\). Then

• A. \(R_1 = \sqrt{K}R\)
• B. \(R_1 = R\)
• C. \(R_1 = \frac{R}{K}\)
• D. \(R_1 = \frac{R}{\sqrt{K}}\)

Hint:

A dielectric reduces the force by K, so the distance must shrink by root K to restore the force.

Answer 1

The Correct Option is D

Step 1: Approach
Compare force ratios.

Step 2: Ratio
Same charges: $\dfrac{F_{medium}}{F_{air}}=\dfrac{R^2}{KR_1^2}$. Setting this to 1 gives $R_1^2=\dfrac{R^2}{K}$.

Step 3: Result
$R_1=\dfrac{R}{\sqrt K}$. Option (D).

Final Answer:
The force in the dielectric is k q1 q2 over K R1 squared, so R1 must equal R over root K, option (D). \[ \boxed{R_1=\frac{R}{\sqrt{K}}} \]