# Electric field inside sphere

## Homework Statement

Draw the electric field inside a uniformly-charged nonconducting sphere of total charge Q and radius R.

## Homework Equations

\begin{align*} E &= \frac{Q}{r^2} \quad (r \geq R)\\ E &= \frac{Qr}{R^3} \quad (r < R) \end{align*}

## The Attempt at a Solution

I don't know how to draw the field inside the sphere. The number of field lines should increase as one goes from zero to R, so that if one draws spheres of increasing radii inside the nonconducting sphere, there should be more and more field lines. My best guess is shown in the attachment.

#### Attachments

• IMG.jpg
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## Answers and Replies

is it a hollow or solid sphere

The sphere is solid.

I'd write what you said here and call it good. You're image is just suppose to represent the concept that you conveyed about increased field lines as r increases from 0 to R.
When I've had to do stuff like this I just draw some lines then double on the next set then double on the next just to emphasize the point.

Field lines should start on a charge and either end on a charge or go on to infinity.

The density of the field lines ideally indicating the magnitude of the E field.

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I don't know what your teachers are looking for but here are some comments....

+ve:Both of your drawings show the symmetry of the system.

+ve:Your drawing for the field outside the sphere incorporates the inverse square law too.

-ve:Your drawing for the inside of the sphere is not indicating that the field is proportional to r.

-ve:The two drawings are not indicating that the field is the same at the boundary r=R

As to how to improve your drawing: a single figure would be better. Focus upon achieving this from your original post
The number of field lines should increase as one goes from zero to R, so that if one draws spheres of increasing radii inside the nonconducting sphere, there should be more and more field lines.
The spheres idea is a great place to start, so try with say four thin spheres: the surface and three equi-spaced internal thin spheres at R/4, R/2 and 3R/4.

[edit: I don't think it is possible to produce a perfect answer in the drawing, I know I'd want to supplement the field drawing I made with a graph of magnitude(E) vs r or a graph of E along a line through the middle of the sphere]

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Thanks for your help Bumble and NoPoke. It's much clearer now!
Here is a revised drawing. Does this look more accurate?

#### Attachments

• IMG.jpg
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yes, but make all the field lines end at the same distance away from the center as they are supposed to go on to infinity.