Final answer:
To find the electric field 1.4 m from the axis of an infinite cylindrical shell with a given surface charge density, one applies Gauss's law. A Gaussian surface is chosen and the charge enclosed is determined. The electric field magnitude can then be calculated and is found to be uniform and directed radially outward from the cylinder.
Step-by-step explanation:
The student’s question is related to the calculation of the electric field due to a charged infinite cylindrical shell by applying Gauss's law. Since the radius of the cylindrical shell is 0.45 m and the point of interest is at 1.4 m from the axis (which is outside the shell), and knowing that the surface charge density is 1.4 pC/m², the electric field can be determined using Gauss's law for a cylinder.
To find the electric field at a point outside the cylinder, we consider a Gaussian surface that is a coaxial cylinder with the given cylindrical shell and with a radius larger than that of the shell. The length of the Gaussian surface should be finite but the actual length does not matter because the charge per unit length is constant for an infinite cylinder.
The total charge enclosed by the Gaussian surface can be obtained by multiplying the length of the Gaussian cylinder by the charge per unit length (which is a product of the surface charge density and the perimeter of the base of the cylindrical shell).
Applying Gauss's law, which states that the net electric flux through a closed surface is equal to the charge enclosed divided by the permittivity of free space, we can set up the equation Φ = E • 2π•r•L = σ•2π•R•L/ ε₀, where Φ is the electric flux, E is the electric field magnitude, r is the radial distance from the axis (1.4 m), and L is the length of the Gaussian surface. Solving for E will give the electric field at a point 1.4 m from the axis of the cylinder.
Since the value of the electric field only depends on the charge enclosed and not on the specific location outside the cylindrical shell, the electric field is uniform and directed radially outward from the cylinder. Thus the magnitude of the electric field can be found using:
E = (σ•2π•R) / (ε₀•2π•r)