Question

Two spherical conductors of capacities 4 µF and 3 µF are charged to same potential having radii 4 cm and 3 cm respectively. If ‘σ₁’ and ‘σ₂’ represent surface density of charge on respective conductors then ______.

विकल्प

• 2 : 3

• 2 : 5

• 3 : 4

• 4 : 7

Answer 1

Two spherical conductors of capacities 4 µF and 3 µF are charged to same potential having radii 4 cm and 3 cm respectively. If ‘σ₁’ and ‘σ₂’ represent surface density of charge on respective conductors then 3 : 4.

Explanation:

For a spherical conductor, surface charge density:

σ = `Q/(4 pi R^2)`

Also, Q = CV. Since both are at the same potential (V):

Q ∝ C

Thus,

σ ∝ `C/R^2`

`sigma_1/sigma_2 = (C_1//R_1^2)/(C_1//R_2^2)`

= `(4//(4)^2)/(3//(3)^2)`

= `(4//16)/(3//9)`

= `(1//4)/(1//3)`

= `3/4`