If the axes of the two cylinders are parallel, but displaced from each other by a distance d, determine the resulting electric field in the region r> r3, where the radial distance r is measured from the metal cylinder's axis. assume d< (r2−r1). express your answer in terms of the variables ρe, r1, r2, r3, d, r, and appropriate constants.

E =  ρ ( R1²) / 2 ∈o R

Explanation:

Given data

two cylinders are parallel

distance = d

radial distance = R

d < (R2−R1)

to find out

Express answer in terms of the variables ρE, R1, R2, R3, d, R, and constants

solution

we have two parallel cylinders

so area is 2 R × l

and we apply here gauss law that is

EA = Q(enclosed) / ∈o   ......1

so first we find  Q(enclosed) = ρ Volume

Q(enclosed) = ρ ( R1² × l )

so put all value in equation 1

we get

EA = Q(enclosed) / ∈o

E(2 R × l)  = ρ ( R1² × l ) / ∈o

so

E =  ρ ( R1²) / 2 ∈o R

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