Two long concentric cylindrical shells are both centered on a long wire. The lon

Question

Two long concentric cylindrical shells are both centered on a long wire. The long wire has a constant charge density = 211 microcoulombs per meter. The smaller cylinder has a radius of 5 centimeters and has a constant charge density that appears from the outside as = - 211 microcoulombs per meter. The larger cylinder has a radius of 8 centimeters and has a constant charge density that appears from the outside as = 211 microcoulombs per meter.
a) Find the magnitude of the electric field at a distance of 1 centimeters from the central wire.
b) Find the magnitude of the electric field at a distance of 6.63 centimeters from the central wire.
c) Find the magnitude of the electric field at a distance of 12.24 centimeters from the central wire.

Explanation / Answer

long wire: 1 = 211 C/m,

smaller cylinder: a = 5 cm, 2 = -211 C/m

larger cylinder: b = 8 cm, 3 = 211 C/m

a) Find the magnitude of the electric field at a distance of r = 1 cm.

use Gauss law,

E*2rL = 1L/0

E = 1/(20r) = 3.79*108 N/C
b) Find the magnitude of the electric field at a distance of 6.63 cm.

E*2rL = (1 + 2)L/0

E = 0

c) Find the magnitude of the electric field at a distance of 12.24 cm

E*2rL = (1 + 2 + 3)L/0

E = 3/(20r) = 3.10*107 N/C

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