Suppose the electric field in some region is found to be e = kr3 ˆr, in spherical coordinates (k is some constant). (a) find the charge density rho. (b) find the total charge contained in a sphere of radius r, centered at the origin. (do it two different ways.)

Part a)

Part b)

Explanation:

Part a)

As we know that electric field intensity due to some given charge distribution is given as

now electric flux through a spherical surface of radius r is given as

now by Guass law we know that

now volume charge density is given as

Part b)

Total charge inside the radius R is given as

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