Find the magnitude of the electric field for r>b Nested Shells 2A solid sphere with radius a has a charge distribution of p(r) = (1/(47)) · (5r2 + 4a · r) for r < al. This solid sphere is enclosed by an infinitely thin spherical shell of radius b.The outer shell has a surface charge density of o = -Q/(4T · b² ) where Q| is the total amount of charge found on the inner sphere.ab

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College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Find the magnitude of the electric field for r>b

Nested Shells 2
A solid sphere with radius a has a charge distribution of p(r) = (1/(47)) · (5r2 + 4a · r) for r < al. This solid sphere is enclosed by an infinitely thin spherical shell of radius b.
The outer shell has a surface charge density of o = -Q/(4T · b² ) where Q| is the total amount of charge found on the inner sphere.
a
b

Expert Solution

Step 1

Let us assume a Gaussian surface of spherical symmetry having radius r such that r > b.

The electric flux through the surface can be represented as,

Here, E, da, Q_e, and ε₀ represent the electric field, the surface’s area element, the charge inside the surface, and the free space’s permittivity, respectively.

the charge inside the Gaussian surface cab be determined as,

Here, Q_S and Q_Sh represent the sphere’s charge and the shell’s charge, respectively.

The shell’s charge can be determined as,

Here, σ and A represent the shell’s surface charge density and the shell’s surface area, respectively.

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