Electric filed:

E = kQ/r^{2}

R_{1} = 8cm(1m/100cm) = 0.08m

r = 0.5(R_{1} + R_{2}) = 0.5(8 + 15) = 11.5 cm (1m/100cm) = 0.115 m

Q_{point charge} = - 45 nC(10^{-9}C/1nC) = - 45 × 10^{-9} C

${\mathit{Q}}_{\mathbf{e}\mathbf{n}\mathbf{c}\mathbf{l}\mathbf{o}\mathbf{s}\mathbf{e}\mathbf{d}}\mathbf{=}{\mathit{Q}}_{\mathbf{p}\mathbf{o}\mathbf{i}\mathbf{n}\mathbf{t}\mathbf{}\mathbf{c}\mathbf{h}\mathbf{a}\mathbf{r}\mathbf{g}\mathbf{e}}\mathbf{}\mathbf{+}\mathbf{}{\mathit{Q}}_{\mathbf{s}\mathbf{p}\mathbf{h}\mathbf{e}\mathbf{r}\mathbf{e}}$

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}

What is the radial electric field at the point r =0.5(R_{1}+R_{2})? Give your answer in the units of kN/C

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