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Use Gauss's law to prove that the electric field outside any spherically symmetric charge distribution is...

Use Gauss's law to prove that the electric field outside any spherically symmetric charge distribution is the same as if all of the charge were concentrated into a point charge at the center of the sphere. Then use Gauss's law to prove that the electric field inside a spherically symmetric conductor carrying a net charge on its surface is zero.

Expert Solution

Consider a charge distribution having charge 'Q" uniformly distrubuted

Consider a gassian surface of radius 'r' outside the charge distribution .

According to gauss's law

E. A = q_enclosed / _o

enclosed charge inside the gaussian surface = Q

Area of gaussian surface = A = 4r²

E (4r²) = Q/ _o

E = Q/ (4_o r²)

Consider a gassian surface of radius 'R' inside the charge distribution .

According to gauss's law

E. A = q_enclosed / _o

enclosed charge inside the gaussian surface = 0, (since there is no charge inside)

Area of gaussian surface = A = 4r²

E (4r²) = 0/ _o

E = 0

genius_generous answered 1 hour ago

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