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An insulating sphere is 4.00 cm in radius and carries a 5.80 µC charge uniformly distributed throughout its interior volume. Calculate the charge enclosed by a concentric spherical surface with the following radius. (a) r = 3.00 cm nC (b) r = 7.00 cm

An insulating sphere is 4.00 cm in radius and carries a 5.80 µC charge uniformly distributed throughout its interior volume. Calculate the charge enclosed by a concentric spherical surface with the following radius. (a) r = 3.00 cm nC (b) r = 7.00 cm

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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An insulating sphere is 4.00 cm in radius and carries a 5.80 µC charge uniformly distributed throughout its interior volume. Calculate the charge enclosed by a concentric spherical surface with the following radius. (а)r %3D 3.00 сm nC (b) r = 7.00 cm
Transcribed Image Text:An insulating sphere is 4.00 cm in radius and carries a 5.80 µC charge uniformly distributed throughout its interior volume. Calculate the charge enclosed by a concentric spherical surface with the following radius. (а)r %3D 3.00 сm nC (b) r = 7.00 cm
Expert Solution
Step 1

If an amount of charge Q is distributed throughout the interior volume of an insulator of radius R, its volume charge density is given by

ρ=Qv

⇒ρ=Q43πR3

Now amount of charge enclosed by a concentric sphere of radius r (r<R) is 

q=ρ×43πr3 

Substituting the value ρ of from the above we get

q=Q43πR3×43πr3

q=Qr3R3 ....................(1)

But when r>R then total charge enclosed by the concentric sphere is

q=Q..................(2)

 

Data Given:-

Total charge on the insulating sphere is Q=5.80 μC=5.80×10-6 C

Radius of the insulating sphere is R=4.00 cm=0.04 m

Radius of the first concentric sphere is r=3.00 cm=0.03m

Radius of the second concentric sphere is r=7.00 cm=0.07 m

 

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