A solid sphere of radius a = 2.0 cm has a uniform net charge of q1 = 5.0 fC (= 5

Question

 A solid sphere of radius a = 2.0 cm has a uniform net charge of q1 = 5.0 fC (= 5.0x10^{-15} Coul). It is surrounded by a concentric spherical conducting shell, with inner radius b = 4.0 cm and outer radius c = 4.8 cm. The conducting shell has a net charge of q2 = - q1 = -5.0 fC.  Find the radial electric field at the following locations: a) r = 0 b) r = 1 cm c) r = 2 cm d) r = 3 cm e) r = 4.6 cm f) r = 7.0 cm  Also, find the net charge on the inner surface (radius b), and the net charge on the outer surface (radius c), of the shell. 

Explanation / Answer

here Qnet due to concentric shells = q1+q2 = 5fc - 5fc = 0

so

a. ELectric field at r = 0 is 0

b. EF at a point inside the sphere E = KQr/ a^3

EF = 9*10^9 * 5*10^-15 * 0.01/0.02^3

EF = 0.056 N/C

c. EF on the surface of the sphere E = KQ/a^2

E = (9e9 * 5e -15)/(2e-2* 2e-2)

E = 0.112 5N/C

d. E at 3 cm = (9e9 * 5e -15/(0.03 *0.03)

E = 0.05 N/C

E. E outide the sphere = (9e9 * 5e -15/(0.046 * 0.046)

E = 0.0212 N/C

f. E at 7cm = 9e9 * 5e-15/(0.07 * 0.07)

E = 0.00918 N/C

qNet = q1+q2 = 5fc - 5fc = 0

on inner surface it is 5fc

outer surface = - 5 fc

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