The goal of this problem is to find the electric field inside of a cavity which is cut into a uniformly charged sphere. Inside of the cavity, there is no charge, but this cavity is off- center. To do this, we will consider it as a solid, uniformly positively charged sphere (with no cavity) added to a solid, uniformly negatively charged sphere such that +Po – Po = 0 in the space where the two spheres coexist. But in order to add the two fields, they have to be calculated from the same origin (see part (c) for more on that). (a) Find the electric field inside of a sphere with uniform charge density, po, which is located at the origin. (b) Find the electric field inside of a sphere with uniform charge density, -po, which is located at the origin. (c) If we shift the negatively charged sphere from part (b) to be centered at a position d rather than the origin, what is the location of a random point inside of your negatively charged sphere as measured from the origin (7)? Express this answer in terms of the location of the center of the negatively charged sphere (ā) and the location of the random point measured from the center of the negative sphere (F")I (d) Use parts (a), (b), and (c) to find the electric field inside of a cavity in a uniformly charged sphere.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Please answer all parts.

-When you spin the 2-D version of that shape, the center of mass travels upwards and the hole goes to the bottom as it is spinning.

Hint: The easiest way to go about this is to mark three points in a drawing: (1) the origin, (2) the center of your sphere [no longer at the origin], (3) a random point inside of your sphere [the more random the better]. You will then need to construct a triangle of vectors which include: (1) the vector~R(going from the origin to the center of your sphere), (2) the vector going from the origin to your random point (~r), and (3) the vector going from the center of your sphere to your random point (~r1).

The goal of this problem is to find the electric field inside of a cavity which is cut into
a uniformly charged sphere. Inside of the cavity, there is no charge, but this cavity is off-
center. To do this, we will consider it as a solid, uniformly positively charged sphere (with
no cavity) added to a solid, uniformly negatively charged sphere such that +po – Po = 0 in
the space where the two spheres coexist. But in order to add the two fields, they have to be
calculated from the same origin (see part (c) for more on that).
(a) Find the electric field inside of a sphere with uniform charge density, p, which is
located at the origin.
(b) Find the electric field inside of a sphere with uniform charge density, -po, which is
located at the origin.
(c) If we shift the negatively charged sphere from part (b) to be centered at a position
a rather than the origin, what is the location of a random point inside of your negatively
charged sphere as measured from the origin ()? Express this answer in terms of the location
of the center of the negatively charged sphere (ā) and the location of the random point
measured from the center of the negative sphere ()
(d) Use parts (a), (b), and (c) to find the electric field inside of a cavity in a uniformly
charged sphere.

(d) Use parts (a), (b), and (c) to find the electric field inside of a cavity in a uniformly
charged sphere.

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