A hollow metal sphere has inner radius R_1 = 20 cm and outer radius R_2 = 50 cm

Question

A hollow metal sphere has inner radius R_1 = 20 cm and outer radius R_2 = 50 cm and has a charge of +2.0 mu C. What is the strength of the electric field at the center of the sphere? What is the strength of the electric field 10 cm from the center of the sphere? What is the strength of the electric field 30 cm from the center of the sphere? What is the maximum strength of the electric field caused by the sphere? Where is it found? Graph the electric field E vs. radial distance r. What force would act on an excess electron (q = -1.60 times 10^-19 C) on the outer surface of the sphere? What is the strength of the electric field at a point 60 cm from the center of the sphere? What force would act on an alpha particle (q = +3.20 times 10^-19 C) located 60 cm from the center of the sphere?

Explanation / Answer

inside hallow sphere q = 0

so

E = 0 at the center of the sphere

at r= 10 cm E = 0.

r = 30 cm E = 0.

(11)

E = kq/r^2 = 9*10^9(2* 10^-6 )/(0.5 )^2 = 7.19 * 10^4 N/C

at r= 50 cm we get maximum electric field

(12)

F = Eq = 7.19 * 10^4 N/C(1.6 * 10^-19 C) = 1.15 * 10^-14 N toward the center of the sphere

(13)

E = kq/r^2 = 9*10^9(2* 10^-6 )/(0.6 )^2 = 4.99* 10^4 N/C

(14)

F = Eq = 4.99 * 10^4 N/C(1.6 * 10^-19 C) = 1.6 * 10^-14 N away from the center of the sphere

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