Question

Consider a long cylindrical charge distribution of radius R = 12.0 cm with a uniform charge density of rho = 18.0 C/m3. Find the electric field (in N/C) at a distance r = 33.0 cm from the axis. (Enter the magnitude.)

Answer 1

Electric field,
`E=4.43* 10^(10)\ N/C`

Step-by-step explanation:

It is given that,

Radius of the cylinder, R = 12 cm = 0.12 m

Charge density,
`\rho=18\ C/m^3`

Let E is the electric field at a distance of r = 33 cm or 0.33 m from the axis. The relationship between the linear charge density and the volume charge density is given by :

`\lambda=\rho* \pi r^2`

Now according to Gauss's law :

`E.2\pi rl=(\lambda l)/(\epsilon_o)`

`E=(\lambda)/(2\pi \epsilon_or)`

or

`E=(\rho R^2)/(2\epsilon_o r)`

`E=(18* (0.12)^2)/(2* 8.85* 10^(-12)* 0.33)`

`E=4.43* 10^(10)\ N/C`

Hence, this is the required solution.