Question

2. Consider a spherical distribution of charge that creates a uniform, radial electric field described by: E = E_o * r. Use the differential form of Gauss's Law to derive an expression for the radial charge distribution, ρ(r), that will create this field. You will need the divergence in spherical coordinates: ∇⋅V = 1/r^2 * ∂/∂r(r^2V_r) + 1/r * sin[θ] * ∂/∂θ(sin[θ]V_θ) + 1/r * sin[θ] * ∂/∂ϕ(V_ϕ). Enter your mathematical expression for ρ(r) in terms of ε_o, E_o, and r. Type out "epsilon_o" and "E_o", using a lowercase letter "o" for the subscript in both cases. Please note: Each of the following will be interpreted as a single variable, not as a product of variables: epsilon_0, E_0. To multiply variables, please use * (e.g. enter x*y to multiply variables x and y).

          2. Consider a spherical distribution of charge that creates a uniform, radial electric field described by: E = E_o * r. Use the differential form of Gauss's Law to derive an expression for the radial charge distribution, ρ(r), that will create this field. You will need the divergence in spherical coordinates: ∇⋅V = 1/r^2 * ∂/∂r(r^2V_r) + 1/r * sin[θ] * ∂/∂θ(sin[θ]V_θ) + 1/r * sin[θ] * ∂/∂ϕ(V_ϕ). Enter your mathematical expression for ρ(r) in terms of ε_o, E_o, and r. Type out "epsilon_o" and "E_o", using a lowercase letter "o" for the subscript in both cases. Please note: Each of the following will be interpreted as a single variable, not as a product of variables: epsilon_0, E_0. To multiply variables, please use * (e.g. enter x*y to multiply variables x and y).

Added by Bryan P.

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