Two metallic sphere having radius 0.2m and 0.3m are charged to the same potential. And the ratio of surface densities of charge on them.
Answers
Answer:
2.25
Explanation:
two metallic spheres
given R*1=0.2m. R*2=0.3m
(R*1/R*2)*2= THEN
0.2*0.2=0.04 0.3*0.3=0.09
(R"2/R"1)"2=0.09/0.04=2.25
Given: the radii of two metallic spheres, r₁ = 0.2m, and r₂ = 0.3m
To Find: the ratio of surface charge density, R = σ₁ /σ₂
Solution:
To calculate R, the formula used:
- σ = q / 4π r²
- Here, σ is the surface charge density
q is the charge on the metallic sphere
r is the radius of the metallic sphere
Applying the above formula:
For metallic sphere 1:
σ₁ = q / 4π r₁²
= q / 4π (0.2)²
= q / 4π x 0.04 ⇒ 1
For metallic sphere 2:
σ₂ = q / 4π r₂²
= q / 4π (0.3)²
= q / 4π x 0.09 ⇒ 2
On dividing equations 1 and 2:
σ₁ / σ₂ = (q / 4π x 0.04) / (q / 4π x 0.09)
= 0.09 / 0.04
= 9x100 / 4x100
= 9 / 4
σ₁ / σ₂ = 9 / 4
Hence, the ratio of surface charge densities is 9/4.