In the figure a nonconducting spherical shell of inner radius a = 2.23 cm and outer radius b = 2.70 cm has (within its thickness) apositive volume charge density p = A/r, where A is a constant and r is the distance from the center of the shell. In addition, a small ball ofcharge q = 46.7 fC is located at that center. What value should A have if the electric field in the shell (a srsb) is to be uniform?

Answered: In the figure a nonconducting spherical…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

In the figure a nonconducting spherical shell of inner radius a = 2.23 cm and outer radius b = 2.70 cm has (within its thickness) a
positive volume charge density p = A/r, where A is a constant and r is the distance from the center of the shell. In addition, a small ball of
charge q = 46.7 fC is located at that center. What value should A have if the electric field in the shell (a srsb) is to be uniform?

Expert Solution

Step 1

The electric field within the region of the shell is said to be uniform.

Imagine a Gaussian surface having a radius r, concentric with the center of the given shell. This radius (a<r<b)

So the Gaussian surface lies within the shell of the non conducting sphere.

From Gauss' law, the electric field within this Gaussian surface of radius r is given as

$\oint E . d S = \frac{q_{e n c}}{ε_{o}} E i s t h e e l e c t r i c f i e l d d S i s a s u r f a c e e l e m e n t o f t h e g a u s s i a n s u r f a c e q_{e n c} i s t h e t o t a l c h a r g e e n c l o s e d b y t h e g a u s s i a n s u r f a c e$