A very long straight wire has charge per unit length 1.49×10-10 C/m. At what distance from the wire is the magnitude of the electric field equal to 2.49 N/C? Use 8.85×10-12 C^2/(N*m^2) for the permittivity of free space and use pi = 3.1416 for E = (lambda)/(2*pi*permittivity of free space*r). Given: E = 2.49 N/C I have no idea what to do with this formula. Why is wavelength needed and what is the variable we are trying to find? I am lost. Thanks.
In this formula, lambda stands for the "charge per unit length", not wavelength. You are trying to find the distance from the wire, which is "r".
[itex] \lambda [/itex] is not a wavelength,it's the linear charge density and it's measured in C/m. Plug in all the numbers in the formula & see what happens... Daniel.