Question

A conducting sphere of radius 5cm is charged 15 muC

Answer 1

Complete Question:

A conducting sphere of radius 5 cm is charged to 15 uC. Another uncharged sphere of radius 10 cm is allowed to touch it for enough time. After the two are separated, the surface density of charge on the two spheres will be in the ratio?

Correct Solution:

Given:

R1 = 5 cm

R2 = 10 cm

Q1 = 15 uC

To Find:

Ratio of surface charge density of the two spheres.

Calculation:

- After redistribution, the charge on the spheres are:

Q1' = (5×15)/(5+10) = 5 uC

Q2' = (10×15)/(5+10) = 10 uC  

- Ratio of surface charge densities is givren as:

σ1/σ2 = (Q1'/Q2') × (R2²/R1²)

⇒ σ1/σ2 = (5/10) × (10/5)² = 10/5

⇒ σ1/σ2 = 2 / 1

- So, the ratio of surface charge density of the two spheres is 2 : 1.