Question

A team of storm physicists is attempting to replicate lightning by charging two long cables stretched over a canyon, as shown. One cable will attain a highly positive and uniform charge density of  +𝜆,  and the other will attain the same amount of charge density but opposite in sign (i.e.,  −𝜆).  Since the appearance of lightning directly depends on the electric field strength created by charge separation, they must derive an expression for electric field strength between the two cables.

The cables are sufficiently long to be approximated as infinitely long. Calculate the magnitude of the electric field strength  𝐸  between the two cables as a function of  𝜆  (the linear charge density) and  𝑟  (the distance from the positively charged cable). Use  𝜖0  as the permittivity of free space, and assume the wires are separated by a distance  𝐷.