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ating sphere of radius R and total charge Q has a spherically symmetric 6 but non-uniform charge density given by p= Ar where A is a constant and ris measured from the center of the sphere. Calculate the electric field at any radius r within the sphere (i.e. for r

ating sphere of radius R and total charge Q has a spherically symmetric 6 but non-uniform charge density given by p= Ar where A is a constant and ris measured from the center of the sphere. Calculate the electric field at any radius r within the sphere (i.e. for r

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A solid insulating sphere of radius R and total charge Q has a spherically symmetric but non-uniform charge density given by p= Ar where A is a constant and r is measured from the center of the sphere. Calculate the electric field at any radius r within the sphere (i.e. for r<R) Q/(4π ερ 12) (Ar²)/(980) (Ar³)/(5 &0) (Ar5)/(5 R²80) Q/(4π 0 R²)
Transcribed Image Text:A solid insulating sphere of radius R and total charge Q has a spherically symmetric but non-uniform charge density given by p= Ar where A is a constant and r is measured from the center of the sphere. Calculate the electric field at any radius r within the sphere (i.e. for r<R) Q/(4π ερ 12) (Ar²)/(980) (Ar³)/(5 &0) (Ar5)/(5 R²80) Q/(4π 0 R²)
Expert Solution
Step 1

Given: The radius of the insulating sphere is R. 

           The total charge is Q . 

           The charge density is Ar6.

To determine: The electric field at r<R

Assume a gaussian surface at radius r. 

The charge enclosed in gaussian surface is 

q=∫0rρdV

The volume element is dV=4πr2dr

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