please explain the solutions. hollow metal sphere has inner and outer radii or 2
ID: 779127 • Letter: P
Question
please explain the solutions.
hollow metal sphere has inner and outer radii or 20.0 cm and 30.0 cm' respectively. As shown in the figure, a solid metal sphere of radius 10.0 cm is ocated at the center of t hollow sphere. The electric field at a point P, a distance of 15.0 cm from the center, is found to be El-4.61-104 N/C, directed radially inward. At point Q, a distance or 35.0 cm from the enter, the electric field is found to be E2-4.61-104 N/C, directed radially outward. 30.0 c a)Determine the total charge on the surface of the inner sphere. 0 cm 15.0 cm P cim o) Determine the total charge on the inner surface of the hollow sphere. Cevaby onayla Tries /s ) Determine the total charge on the outer surface of the hollow sphere. E, 35.0 Tries o/s E2Explanation / Answer
a)
By Gauss' Law,
E1 dA = q / (o)
(E1)(4r²) = q / (o)
(-4.61e4 N/C)(4(0.150 m)²) = q / (8.85e-12 C²/N-m²)
q = -1.15e-7 C or -115 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 = +1.15e-7 C or +115 nC
c)
The sum of the charges on the other 2 surfaces is zero, so
E2 dA = q / (o)
(E2)(4r²) = q / (o)
(+4.61e4 N/C)(4(0.350 m)²) = q / (8.85e-12 C²/N-m²)
q = +6.28e-7 C or +628 nC
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