Question

What are (a) the charge and (b) the charge density on the surface of a conducting sphere of radius 0.20 m whose potential is 240 V (with V = 0 at infinity )?

Answer 1

(a) charge q=5.33 nC

(b) charge density σ=10.62 nC/m²

Step-by-step explanation:

Given data

radius r=0.20 m

potential V=240 V

coulombs constant k=9×10⁹Nm²/C²

To find

(a) charge q

(b) charge density σ

Solution

For (a) charge q

As

`V_(potential)=kq/r\\ q=rV_(potential)/k\\q=((0.20)(240))/(9*10^(9) )\\ q=5.333*10^(-9)C\\or\\ q=5.33nC`

For (b) charge density

As charge density σ is given as:

σ=q/(4πR²)

σ=(5.333×10⁻⁹) / (4π×(0.20)²)

σ=10.62 nC/m²