A hollow metal sphere has inner and outer radii of 20.0 cm and 30.0 cm, respecti

Question

A hollow metal sphere has inner and outer radii of 20.0 cm and 30.0 cm, respectively. As shown in the figure, a solid metal sphere of radius 10.0 cm is located at the center of the hollow sphere. The electric field at a point P, a distance of 15.0 cm from the center, is found to be E1 = 8.11·104 N/C, directed radially inward. At point Q, a distance of 35.0 cm from the center, the electric field is found to be E2 = 8.11·104 N/C, directed radially outward.

a) Determine the total charge on the surface of the inner sphere.

b) Determine the total charge on the surface of the inner surface of the hollow sphere.

c) Determine the total charge on the surface of the outer surface of the hollow sphere.

Please show calculations.

Explanation / Answer

a)
By Gauss' Law,
E1 dA = q / (o)
(E1)(4r²) = q / (o)
(-8.11e4 N/C)(4(0.150 m)²) = q / (8.85e-12 C²/N-m²)
q = -2.03 *10^-7 C or -203 nC

b)
Since the electric field inside a Gaussian surface inside the conducting hollow sphere is zero, the enclosed charge (on the inner sphere and on the inner surface of the hollow sphere) is also zero.
q = +2.03 *10^-7 C 203 nC

c)
The sum of the charges on the other 2 surfaces is zero, so
E2 dA = q / (o)
(E2)(4r²) = q / (o)
(8.11e4 N/C)(4(0.350 m)²) = q / (8.85e-12 C²/N-m²)
q = +1.105*10^-7 C or +110.5 nC

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