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To find the charge enclosed by a sphere of charge density ρ and radius a, you can use the formula for the charge, which is given by:
[ Q = rho cdot V ]
where ( V ) is the volume of the sphere. The volume ( V ) of a sphere is calculated using the formula:
[ V = frac{4}{3} pi r^3 ]
Substituting the radius ( a ) into the volume formula gives:
[ V = frac{4}{3} pi a^3 ]
Therefore, the total charge ( Q ) enclosed within the sphere is:
[ Q = rho cdot frac{4}{3} pi a^3 ]
So, the charge enclosed by the sphere is:
[ Q = frac{4}{3} pi rho a^3 ]
Answer: b
Explanation: The charge enclosed by the sphere is Q = ∫∫∫ ρ dv.
Where, dv = r2 sin θ dr dθ dφ and on integrating with r = 0->a, φ = 0->2π and θ = 0->π, we get Q = ρ(4πa3/3).