The figure shows a spherical shell with uniform volume charge density ? = 1.96 n

Question

The figure shows a spherical shell with uniform volume charge density ? = 1.96  nC/m3, inner radius a = 10.4 cm, and outer radius b = 3.20a. What is the magnitude (in N/C) of the electric field at radial distances (a)r = 0; (b)r = a/2.00, (c)r = a, (d)r = 1.50a, (e)r = b, and (f)r = 3.00b?

(a)
N/C The figure shows a spherical shell with uniform volume charge density ? = 1.96 nC/m3, inner radius a = 10.4 cm, and outer radius b = 3.20a. What is the magnitude (in N/C) of the electric field at radial distances (a)r = 0; (b)r = a/2.00, (c)r = a, (d)r = 1.50a, (e)r = b, and (f)r = 3.00b?

Explanation / Answer

Gauss Law : If there is a charge q enclosed inside any imaginary surface area, then integral of E.ds over the complete area will be equal to charge q divided by epsilon0

(undefined)

Case a) r = 0

Assume an imaginary sphere of radius zero at the centre.

Enclosed charge = 0

E X Area = 0

Thus, E = 0

Case b) r = a/2

Enclosed charge = 0

Therefore E = 0

Case c) r = a

Enclosed charge = 0

E = 0

Case d) r = 1.5a = 1.5 X 11.6 cm = 0.174 m

Enclosed charge = (undefined)

= 0.0287 nC

(undefined)

E = 8.528 SI units

Case e) r = b = 5.3a = 0.6148 m

Enclosed charge = 53 Enclosed charge = (undefined)

= 1.788 nC = 1.788 nC

1.788 1.788 (undefined)

E = 42.5374 SI units E = 42.5374 SI units E = 42.5374 SI units

Case f) r = 3b = 1.8444 m Case f) r = 3b = 1.8444 m Case f) r = 3b = 1.8444 m

Enclosed charge = same as previous question = 1.788 nC Enclosed charge = same as previous question = 1.788 nC Enclosed charge = same as previous question = 1.788 nC

1.788 1.788 1.788 (undefined)

E = 4.73 SI units E = 4.73 SI units E = 4.73 SI units E = 4.73 SI units

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