An infinite line charge of uniform density l = 4 µC/m runs along the symmetry ax

Question

An infinite line charge of uniform density l = 4 µC/m runs along the symmetry axis(z-axis) of a thin, infinitely long, non-conductingcylindrical shell of radius a1 = 0.1 m. Thelatter carries a uniform charge density s1 = 3 µC/ m2.Surrounding the latter and concentric with it is a thick,infinitely long, conducting cylindrical shell with inner radiusa 2 = 0.6 m and outer radiusa3 = 0.7 m. The conducting cylinder isuncharged.

(a) Calculate the charge per unit length on the non-conductingshell.

l1 = C/m    

(b) Calculate the electric field at the following values ofr, where r is the radial distance measuredperpendicularly from the symmetry axis.

At r = 0.05 m:

E = N/C    

At r = 0.35 m:

E = N/C    

At r = 0.65 m:

E = N/C    

At r = 1.4 m:

E = N/C    

Explanation / Answer

l = 4 µC/m, a1= 0.1 m. o1 = 3 µC/ m2.a2 = 0.6 m, a3 = 0.7 m. a) on the conducting shell, charge on length L isl1 * L = 1* (2a1L) l1 = 1* (2a1) = 1.88 C/m = 1.88*10-6C/m b) use Gauss law, E * (2rL) = Q/o =l *L/o E = l /(2or) At r = 0.05 m, l = l, E = l/(2or) = 1.44*106 N/C At r = 0.35 m, l = l +l1, E = (l+ l1)/(2or) = 3.02*105 N/C At r = 0.65 m, E = 0 (inside the conductor) At r = 1.4 m, l = l +l1, E = (l+ l1)/(2or) = 7.56*104 N/C

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