(b) R1 < r < R2 ; What is the E-Magnitude and the Direction? (c) R2 < r < R3 ; W

Question

(b) R1 < r < R2 ; What is the E-Magnitude and the Direction?

(c) R2 < r < R3 ; What is the E-Magnitude and the Direction?

(d) r > R3 ; What is the E-Magnitude and the Direction?

(e) What are the linear charge densities (in terms of ?) on the inner and outer surfaces of the conducting tube?

A very long solid insulated cylinder of radius R1 with a uniform linear charge density per unit length of +7lambda is surrounded by a concentric metal conducting cylindrical tube of inner radius R2 and outer radius R3, as shown in the diagram. The metal tube has a charge per unit length of -5 lambda placed on it. Determine the vector electric field E(r) as a function of distance r from the center of the cylinder for:

Explanation / Answer

lamda--->linear charge density

rho----> volume charge density


lamda = Q/L = Q*pi*R^2/(L*pi*R^2)

lamda = rho*pi*R^2

==> rho = lamda/(pi*R^2)

a) at r<R

E = rho*r/epsilon

E = lamda1*r/(epsilon*pi*R^2)

here lamda1 = 7*lamda

E = 7*lamda*r(epsilon*pi*R^2)

b) at R1<r<R2

E = lamda1/(2*pi*epsilon*r)

E = 7*lamda/(2*pi*epsilon*r)

c) ar R2<2<R3

E = 0( inside conducting material E is always zero)

d) E = (lamda1+lamda2)/(2*pi*epsilon*r)

E = 2*lamda/(epsilon*r)


e) ineerside, -7*lamda

outer side, +2*lamda

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