A spherical volume distribution of charge has a uniform charge density of 2.89*1

Question

A spherical volume distribution of charge has a uniform charge density of 2.89*10^-5C/m^3 and a radius of 18.5 cm.

a) Find the total charge contained in the sphere

b)Using Gauss' Law, find the electric field at its surface

c)Now let's examine the inside of the sphere.Applying Gauss' Law again, find the E Field (Electric field) at a distance of 11.8 from the center of the sphere

d)Now find the electrostatic potential both at the surface of the sphere and at the 11.8cm radius. Explain whats going on with the potential as you go further inside the sphere.

Explanation / Answer

Part a)

Charge density=2.89x10^-5 C/m3, r=18.5 cm=0.185m

So, total charge =Charge densityxVolume of sphere

Volume=4/3x3.14xr^3

=4/3x3.14x(0.185)^3

=0.026m^3

Total charge=2.89x10^-5x0.026

=7.66x10^-7 C

Ans- Total charge is 7.66x10^-7 C

Part b)

Using Gauss Law,

E=q/(4.pi.epsilon.r^2)

E=7.66x10^-7/(4x3.14x8.85x10^-12x(0.185)^2)

E=201578.94 NC

Ans- the electric field at its surface is 201578.94 NC

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