A nonconducting sphere 2.0 m in diameter with its center on the x axis at x = 4

Question

A nonconducting sphere 2.0 m in diameter with its center on the x axis at x = 4 m carries a uniform volume charge of density ? = 3.2

A nonconducting sphere 2.0 m in diameter with its center on the x axis at x = 4 m carries a uniform volume charge of density ? = 3.2 A Mu C/m3. Surrounding the sphere is a spherical shell with a diameter of 4.0 m and a uniform surface charge density ? = -2.1 A Mu C/m2. Calculate the magnitude and direction of the electric field at the following locations. (a) x = 4.9 m, y = 0 .....N/C j i + ....... N/C j (c) x = 2.0 m, y = 3.0 m ....... N/C i + ........ N/C j (b) x = 4 m, y = 1.9 m ........ N/C i + ......N/C

Explanation / Answer

Note that

E = k Qenc / r^2

where

Qenc = the enclosed charge of the Gaussian surface centered at (4, 0) and has the given point on its surface.

r = the distance of the given point from (4, 0)

k = 8.99E9 N *m^2/C^2

Thus, for part A:

It includes only part of the inner sphere:

Qenc = 9.772E-6 C

Thus,

E = 1.08*10^5 N/C i^ + 0 N/C j^   [ANSWER, PART A]

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For part B, it includes it includes all of the inner sphere, and part of the outer sphere.

Qenc = -3.813E-5 C

Thus,

E = 0 N/C i^ + (-9.50*10^4) N/C j^ [ANSWER, PART B]

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For part C, it includes all of the inner sphere, and part of the outer sphere.

Qenc = -3.901E-4 C

Thus,

E = 1.50*10^5 N/C i^ + (-2.24*10^5 N/C) j^ [ASNWER, PART C]

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