# Force on charges inside uniformly charged non-conducting solid sphere

Since the electric field inside a non-conducting uniformly volume charged solid sphere is non-zero, the charges spread in the volume must experience a force. Does that mean after some time, the charges redistribute themselves such that net electric field inside the sphere is $$0$$ $$?$$

• If the sphere is non-conductive, how would you anticipate the charges redistributing themselves? Put another way, if the charges can move around then the material is not non-conductive. Which situation are you asking about? – Guy Inchbald Apr 6 '20 at 12:15
• @GuyInchbald I understand your point. I was actually calculating field inside a non conducting uniformly charged solid sphere from my text and thought about it that since there is a field inside the sphere, the charges present must experience a force. Why do the charges then not move ? What causes them to be in the same place ? – OhMyGauss Apr 6 '20 at 13:51
• You cannot have it both ways. Either it is a non-conductor and charges cannot flow, or charges can move and it is a conductor after all. Are you basically asking what makes a material non-conducting? – Guy Inchbald Apr 6 '20 at 15:40
• @GuyInchbald yes. What makes it non-conducting, what makes the charges fix in one place – OhMyGauss Apr 6 '20 at 16:31

## Pre-requisites

Before we start, we need to know that the charge on a body is due to small charges of a huge amount of atoms/molecules constituting that body. Positive charges are created due to the deficiency of electrons and negative charges are created due to excess of electrons. So electrons are mainly responsible for the charge at a location and the number of protons cannot change so they can't affect the charge. Also, the positive charges/protons are fixed at their locations and cannot move when an external field is applied. All the above statements are true for both, conducting and non conducting materials.

## Explanation

As I can gather from your question and the comments, your question is that why do non conductors not conduct charges and what makes them prevent charge flow. There are, broadly speaking, two types of electrons (in the context of conductivity) associated with an atom, namely, bound electrons and free electrons. The bound electrons are strongly held by the nucleus (positive charges). So when we apply an external electric field, the bounded electrons don't move and stay where they were. But free electrons are not as much bounded to the nucleus as the other species. They are more or less free to move and thus they do so when we apply an external electric field.

## Conclusion

By now you'd have guessed that the conduction is only due to the free electrons and not due to the bound electrons. Thus it simply follows that non conductors/insulators will be lacking free electrons and thus they also lack conductivity. So in case of insulators, the electrons are held so strongly by the nucleus that they don't move when we apply an external electric field.

## Addendum

But this might leave you wondering that if you apply a really really large electric field, you might be able to overcome the nucleus' pull. The answer is yes, you can apply a large enough electric field which will unbound the bounded electrons. See dielectric strength for more. However, the value of electric field required to unbound the bounded electrons is usually very high, as you can expect.

Using the simple assumption $$\vec J=\sigma\vec E$$ and where $$\sigma$$ is the conductivity, Gauss’ law in differential form $$\vec\nabla\cdot\vec E=\rho/\epsilon$$ and the continuity equation \begin{align} \vec\nabla \cdot \vec J=-\frac{\partial \rho(\vec r,t)}{\partial t} \end{align} one shows that the density of charge goes like \begin{align} \rho(\vec r,t)=\rho_0(\vec r)e^{-\sigma t/\epsilon}\, . \end{align} For good dielectrics, $$\sigma\to 0$$ and $$\epsilon$$ remains finite so the charge density decreases arbitrarily slowly.

In practice, the local electric field is not sufficient strong to liberate the electrons from their bound states around the nuclei/atoms/molecules so there is no net movement of charge, i.e. the charge remains constant in any volume.