Answer:
[tex]E = 7.2*10^{10}N/C[/tex]
Explanation:
The differential electric field [tex]dE[/tex] due to differential charge [tex]dQ[/tex] at distance [tex]x[/tex] from the origin is
[tex]dE = k\dfrac{dQ}{x^2}[/tex]
but since [tex]dQ = \lambda dx = 4x^2dx[/tex] we have
[tex]dE = k\dfrac{4x^2dx}{x^2}[/tex]
[tex]dE = 4k\: dx[/tex]
integrating this from [tex]x_0[/tex] to [tex]x_0+L[/tex] we get
[tex]$E = \int^{x_0+L}_{x_0} {4k} \, dx $[/tex]
[tex]E = 4k[(x_0+L)-x_0][/tex]
[tex]E =4kL[/tex]
putting in [tex]k = 9*10^9Nm^2/C^2[/tex] and [tex]L =2m[/tex] we get
[tex]\boxed{E = 7.2*10^{10}N/C.}[/tex]
