Question

1) Two point charges at a distance rin air experience a certain force. Then the distance at which
they will experience the same force in a medium of dielectric constant Kis
a) r/K
b) Kr​

Answer 1

Answer:

Let two point charges q₁ and q₂ are separated r distance form each other.

Then, Force experienced between them , F = q₁q₂/4π∈₀r²

Now, both the charges are placed in a medium of dielectric constant , K = 16

Then, force experienced between them = 4F = q₁q₂/K(4π∈₀r'²)

Put F = q₁q₂/4π∈₀r²

∴ 4q₁q₂/4π∈₀r² = q₁q₂/K(4π∈₀r'²)

⇒ 1/r² = 1/4r'²K

⇒1/r² = 1/4 ×r'² × 16

⇒ 1/r² = 1/(8)²r'²

taking square root both sides,

⇒1/r = 1/8r'

∴r' = r/8

Hence, distance between them in medium = r/8