A long non-conducting cylinder has a charge density p = a r, where a = 8.26 C/m4

Question

A long non-conducting cylinder has a charge

density p = a r, where a = 8.26 C/m4

and r is in meters. Concentric around it is a hollow

metallic cylindrical shell. These are radii.

What is the surface charge density inside the

hollow cylinder?

Answer in units of C/m2

A long non-conducting cylinder has a charge density p = a r, where a = 8.26 C/m4 and r is in meters. Concentric around it is a hollow metallic cylindrical shell. These are radii. What is the surface charge density inside the hollow cylinder?

Explanation / Answer

so net charge in inner cylinder

Q = L*integral of rho 2 pi r dr

=2*pi*L*a integral of r^2 dr from 0 to R

= 2*pi*L*a*R^3/3

so Q/L = 2*pi*8.26*5.06E-2^3/3=0.00224

so the inner surface will have to have the same charge so that Qenc = 0 and thus E in conductor = 0

so charge density = Q/(2 pi r L) = 0.00224/(2*pi*10.2E-2)=0.00350 C/m^2

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