🤓 Based on our data, we think this question is relevant for Professor Becker's class at TAMU.

Gauss' law:

$\overline{){\mathbf{\oint}}{\mathbf{E}}{\mathbf{\xb7}}{\mathbf{d}}{\mathbf{A}}{\mathbf{=}}\frac{\mathbf{Q}}{{\mathbf{\epsilon}}_{\mathbf{0}}}}$

Area of a sphere:

$\overline{){\mathbf{A}}{\mathbf{=}}{\mathbf{4}}{\mathbf{\pi}}{{\mathbf{r}}}^{{\mathbf{2}}}}$

The Gaussian surface is a sphere with a radius of r. We'll use -Q for the charge enclosed.

The closed integral of dA = A

A hollow non-conducting spherical shell has inner radius R_{1 }= 8cm and outer radius R_{2} = 15 cm. A charge Q = - 45 nC lies at the center of the shell. The shell carries a spherically symmetric charge density ρ = Ar for R_{1} < r <R_{2} that increases linearly with radius, where A= 29 μC/m^{4}

Write an equation for the radial electric field in the region r<R_{1} in terms of Q, r and Coulomb's constant k. You may take the positive direction as outward.

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Based on our data, we think this problem is relevant for Professor Becker's class at TAMU.