Find the magnitude of the electric field at a point 4 cm away from a line charge of density `2 xx 10^(-6) C m^(-1)`.

Explanation

Drawing the electric field around line
charge, we find a cylinder of radius
`4 xx (10^-2)m `
Given, `lambda = linear charge density `
` = 2 xx (10^-6)C/m`
we know,
` E.ds = q/epsilon_0`
` E. 2pi rl = lambda l / epsilon_0 `
` E = (lambda / 2 pi r epsilon_0) `
` = (9 xx 2 xx (10^9) xx 2 xx (10^-6)/ 4 xx (10^-2))`
` = 9 xx (10^5) N/C .`