Question

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.

Answer 1

E = ρ ( R1²) / 2 ∈o R

Step-by-step 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
`\pi` 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 (
`\pi` R1² × l )

so put all value in equation 1

we get

EA = Q(enclosed) / ∈o

E(2
`\pi` R × l) = ρ (
`\pi` R1² × l ) / ∈o

so

E = ρ ( R1²) / 2 ∈o R