An infinitely long cylindrical conductor has radius R and uniform surface charge density σ . (a) In terms of σ and R , what is the charge per unit length λ for the cylinder? (b) In terms of σ , what is the magnitude of the electric field produced by the charged cylinder at a distance r > R from its axis? (c) Express the result of part (b) in terms of λ and show that the electric field outside the cylinder is the same as if all the charge were on the axis. Compare your result to the result for a line of charge in Example 22.6 (Section 22.4).
An infinitely long cylindrical conductor has radius R and uniform surface charge density σ . (a) In terms of σ and R , what is the charge per unit length λ for the cylinder? (b) In terms of σ , what is the magnitude of the electric field produced by the charged cylinder at a distance r > R from its axis? (c) Express the result of part (b) in terms of λ and show that the electric field outside the cylinder is the same as if all the charge were on the axis. Compare your result to the result for a line of charge in Example 22.6 (Section 22.4).
An infinitely long cylindrical conductor has radius R and uniform surface charge density σ. (a) In terms of σ and R, what is the charge per unit length λ for the cylinder? (b) In terms of σ, what is the magnitude of the electric field produced by the charged cylinder at a distance r > R from its axis? (c) Express the result of part (b) in terms of λ and show that the electric field outside the cylinder is the same as if all the charge were on the axis. Compare your result to the result for a line of charge in Example 22.6 (Section 22.4).
The charge density of a non-uniformly charged sphere of radius 1.0 m is given as:
For rs 1.0 m; p(r)= Po(1-4r/3)
For r> 1.0 m; p(r)= 0,
where r is in meters.
What is the value of r in meters for which the electric field is maximum?
The volumetric charge density of a cylinder of radius R is proportional to the distance to the center of the cylinder, that is, ρ = Ar when r≤R, with A being a constant.
(a) Sketch the charge density for the region - 3R < r < 3R. What is the dimension of A?b) Calculate the electric field for a point outside the cylinder, r > Rc) Calculate the electric field for a point inside the cylinder, r<R.d) Sketch Exr
The bulk density of charge on a sphere of radius a is given by ρ = ρ0(1 + r/a), where ρ0 is a constant, and r is the radial distance measured from the center of the sphere. (a) Determine the total charge present on the sphere.(b) Calculate the electric field for points inside the sphere.
Chapter 22 Solutions
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