3. A solid sphere of radius R carries a non-uniform volume charge density given by ? = ?0 (r/R)^2, where ?0 is a constant and r < R is measured from the center. a. What is the total charge Q of the sphere? (HINT: Consider breaking the sphere up into spherical shells of thickness dr with a volume of dV = 4? r^2 dr) b. Find the magnitude of the electric field for points r > R c. Find the magnitude of the electric field for points r < R d. What is the potential difference between r = 0 and r = R.
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The charge density is given by Ļ(r) = Ļā(r/R), where Ļā is a constant and r is the distance from the center of the sphere. We can break the sphere into spherical shells of thickness dr and volume dV = 4ĻrĀ²dr. The charge in each shell is given by dq = Ļ(r)dV. So, Show moreā¦
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