# A solid non conducting sphere

• Liquidxlax
In summary, the conversation discusses the calculation of the total charge and electric field for a solid nonconducting sphere with a nonuniform charge distribution. It is shown that the total charge on the sphere is equal to πρsR3 and the electric field inside the sphere can be calculated using (kQr2)/R4. The conversation also mentions the use of an integral to calculate the electric field and the confusion between r and R in the integral setup.
Liquidxlax

## Homework Statement

A solid nonconducting sphere of radius R carries a nonuniform charge distribution, with a charge density ρ = ρsr/R, where ρs is a constant and r the distance from the centre of the sphere. Show that

i) the total charge on the sphere is

Q= πρsR3

and

ii) the electric field inside the sphere is given by

(kQr2)/R4

## Homework Equations

Qenc = integral(dQ) = inetgral(ρdV) = ρintegral(dV) = ρV =

((Q4πr3)/3) / ((4πR3)/3) = Q(r/R)3

## The Attempt at a Solution

dA = 4πR2dr

ρdA = 4πρsrRdr

integrate r from 0 to R but i have a 2 in front.

You're confusing r and R when setting up your integral.

vela said:
You're confusing r and R when setting up your integral.

even when i do it that way, I'm left with 2 in front and then R^2

i really need help with this one. my prof is fluffing everyone off.

Show your work. I'm not sure exactly what you did.

## 1. What is a solid non conducting sphere?

A solid non conducting sphere is a three-dimensional object with a uniform density that does not allow the flow of electrical current.

## 2. How is a solid non conducting sphere different from a conducting sphere?

A solid non conducting sphere does not allow the flow of electrical current, while a conducting sphere allows the flow of electrical current due to its ability to conduct electricity.

## 3. What are some examples of solid non conducting spheres?

Some common examples of solid non conducting spheres include rubber balls, plastic balls, and wooden balls.

## 4. How is the surface charge distributed on a solid non conducting sphere?

The surface charge on a solid non conducting sphere is evenly distributed, as it does not allow for the accumulation of charge on one side.

## 5. What are the applications of a solid non conducting sphere?

Solid non conducting spheres are commonly used in physics experiments and demonstrations, as well as in sports equipment like golf balls and billiard balls.

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