# Insulating Spherical Charged Solid with a Cavity

• dchrisma
In summary, the problem involves a point charge located in the center of a spherical cavity inside an insulating charged solid. The charge density in the solid is given, and the goal is to calculate the electric field at a specific distance from the center of the cavity. Using the equations for electric potential and electric field, the solution involves superposition and is independent of the charge density and size of the cavity.
dchrisma

## Homework Statement

A point charge of -2.09*10^(-6) C is located in the center of a spherical cavity of radius 6.54 cm inside an insulating spherical charged solid. The charge density in the solid is 7.36×10^(-4) C/(m^3) .

Calculate the magnitude of the electric field inside the solid at a distance of 9.48 cm from the center of the cavity.

## Homework Equations

$$\Phi$$= EA = Qenc/$$\epsilon$$0

E = Q/(4(pi)(epsilon sub 0)(r^2)

## The Attempt at a Solution

Bear with me, latex is a bit beyond my capabilities at the moment. I scanned my work. The answer didn't look right and of course, it was not. It also seemed strange not to use the radius of the cavity and even the given charge distribution, but I'm not sure how to incorporate them.

#### Attachments

• scan0003.jpg
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Nobody wants to take a whack at it?

If you imagine the case of cavity being at the center of insulated sphere, the field is zero by symmetry. Use superposition to solve the problem. The fiels is indeed independent of the charge density of the sphere and the size of the cavity.

Surendranath

## What is an "Insulating Spherical Charged Solid with a Cavity"?

An insulating spherical charged solid with a cavity refers to a spherical object made of an insulating material (such as plastic or glass) that has a hollow space or cavity inside. The object also has a net charge, meaning it has an excess or deficit of electrons.

## Why is this topic important in science?

Studying insulating spherical charged solids with cavities is important in understanding the behavior of electric fields and charges. These objects can be used to model real-life systems, such as atoms or planets, and can help us understand how electric charges interact with each other.

## How is the electric field inside the cavity affected by the charge on the sphere?

The electric field inside the cavity is affected by the charge on the sphere in a way that is similar to how the electric field is affected by a point charge. The field inside the cavity will be stronger if the sphere has a higher net charge, and weaker if the sphere has a lower net charge.

## Can an insulating spherical charged solid with a cavity have a net charge of zero?

Yes, an insulating spherical charged solid with a cavity can have a net charge of zero. This can happen if the sphere has an equal number of positive and negative charges, canceling out the net charge.

## What are some real-life applications of studying insulating spherical charged solids with cavities?

Insulating spherical charged solids with cavities have various applications in technology, such as in capacitors or sensors. They can also be used in research to study the behavior of electric fields and charges in different systems.

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