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A nonconducting spherical shell of inner radius R 1 and outer radius R 2 contains a uniform volume charge density ρ throughout the shell. Use Gauss's law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of the sphere. Your answers should be in terms of ρ, R 1, R 2, r, ε0, and π.
(a) r < R 1

Respuesta :

Answer:

E=0

Explanation:

According to Gauss law:

[tex]\int E.dA =\frac{Q_{en}}{\epsilon_o}[/tex]

So, first calculate the amount of charge enclosed in the region where r < R₁.  

Since, the volume charge density is just throughout the shell (i.e. between R₂ and R₁), there is no charge in the region r < R₁. Therefore, [tex]{Q_{en}=0[/tex]

⇒ E = 0 for  r < R₁

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