As a member of a team of storm physicists, you are attempting to replicate light

Question

As a member of a team of storm physicists, you are 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 + lambda and the other will attain the same amount of charge density, but opposite in sign (i.e., - lambda ). Since the appearance of lightning directly depends on the electric field strength created by charge separation, it is important to derive an expression for electric field strength at all points between the two cables (albeit near the midpoint of the wires). The cables are sufficiently long as to be considered (for all practical purposes) infinitely long. Calculate the magnitude of the electric field strength between the two cables as a function of lambda (the linear charge density) and r (the distance from the positively charged cable). Use epsilon 0 as the permitivity of free space and assume the wires are separated by a distance D. If the value of the linear charge density is lambda = 30.5 mu C/m and the distance between the two cables is D = 10.5 m, calculate the electric field midway between the two cables.

Explanation / Answer

a) To calculate the electric field strength:

E.dS = Int of [sum of enclosed charges (q) /eo]

Lambda = charge per unit area (L=1) in other words lambda = q/l = q
lamda = q
ds is the surface area of the wire can be thought of as a very long thin cylinder = 2 x pi x r x l
ds - 2 x pi x r x L

E (2 x pi x r x L) = lambda/ eo
E = Lambda/(2 x pi x r x L x eo)

b) Substituting the values for lambda, r and epsilon, the electric field midway between the two cables= 40*10^-6/ (8.85*10^-12*?*(30/2))= 9.59*10^4 N/C

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