Question

A charge of 4 nc is placed uniformly on a square sheet of nonconducting material of side 17 cm in the yz plane. (a) what is the surface charge density sigma ?

Answer 1

The charge density of the sheet is 1.384×10⁻⁷C/m².

Charge density is defined as the charge per unit area.

The sheet is a square of length l=17 cm.

Calculate the area A of the sheet .

`A=l^2=(17 cm)^2= (17*10^-^2m)^2=0.0289 m^2`

The charge Q on the sheet is

`Q=4nC=4*10^-^9C`

The charge density σ is given by,

`\sigma=(Q)/(A)`

Substitute 4×10⁻⁹C for Q and 0.0289 m² for A.

`\sigma=(Q)/(A)\\ =(4*10^-^9C)/(0.0289 m^2) \\ =1.389*10^-^7C/m^2`

Thus, the charge density of the sheet is 1.384×10⁻⁷C/m².