Two long, charged, thin-walled, concentric cylindrical shells have radii of 3.0

Question

Two long, charged, thin-walled, concentric cylindrical shells have radii of 3.0 and 6.0 cm. The charge per unit length is 5.0 times 10^-6 C/m on the inner shell and -7.0 times 10^-6 C/m on the outer shell. What are the magnitude and direction (radially inward or outward) of the electric field at radial distances (a) r = 4.0 cm and (b) r = 7.0 cm? An early model of the atom had a positive point charge +Ze at the center of a sphere of radius R with uniformly distributed negative charge -Ze. Z is the atomic number, the number of protons in the nucleus, and the number of electrons in the negative sphere. Find (a) an expression for the electric field inside the atom, at a distance r lessthanorequalto R from the center, and (b) the value of the electric field at the surface of the atom. Write your answer in the form of an essay, carefully explaining each of your expressions in terms of Gauss's law.

Explanation / Answer

a) r = 4.0 cm

E (2 pi r l) = lambdai l /e0

E = lambdai /2 pi e0 r

= (5 * 10-6) / (2 pi *8.85 * 10-12 * 4 * 10-2)

= 2.25 * 106 N/C [radially outward]

b) r = 7.00 cm

E (2 pi r l) = (lambda0 + lambdai ) l /e0

= ((-7 + 5 ) * 10-6) / (2 pi *8.85 * 10-12 * 7 * 10-2)

= 5.15 * 105 N/C [radially inward]

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