A spherical insulator of radius R₁ = 10 cm has a spherically-symmetric charge density given by p(r)=r+r². That sphere is centered at the center of a neutral, conductive spherical shell of inner radius R₂ = 19 cm and outer radius R₁ = 21 cm. (a) Find the total charge on the inner sphere. (b) Determine the charge density induced on the inner surface of the conducting shell. (e) Determine the electric field strength i. from r = 0 to r = 10 cm, as a function of r, ii. from r= 10 to r=18 cm, as a function of r, iii. at r = 20 cm, iv. from r = 22 to r= 30 cm, as a function of r.

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A spherical insulator of radius R₁ = 10 cm has a spherically-symmetric charge density given by p(r) = r+r².
That sphere is centered at the center of a neutral, conductive spherical shell of inner radius R₂ = 19 cm and
outer radius R3 = 21 cm.
(a) Find the total charge on the inner sphere.
(b) Determine the charge density induced on the inner surface of the conducting shell.
(c) Determine the electric field strength
i. from r = 0 to r = 10 cm, as a function of r,
ii. from r = 10 to r = 18 cm, as a function of r,
iii. at r = 20 cm,
iv. from r = 22 to r = 30 cm, as a function of r.
(d) Find the electric potential difference between the surface of the inner sphere and the inner surface of the
shell.
Transcribed Image Text:A spherical insulator of radius R₁ = 10 cm has a spherically-symmetric charge density given by p(r) = r+r². That sphere is centered at the center of a neutral, conductive spherical shell of inner radius R₂ = 19 cm and outer radius R3 = 21 cm. (a) Find the total charge on the inner sphere. (b) Determine the charge density induced on the inner surface of the conducting shell. (c) Determine the electric field strength i. from r = 0 to r = 10 cm, as a function of r, ii. from r = 10 to r = 18 cm, as a function of r, iii. at r = 20 cm, iv. from r = 22 to r = 30 cm, as a function of r. (d) Find the electric potential difference between the surface of the inner sphere and the inner surface of the shell.
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