# How electric field changes on changing area of wire?

I know that in an isolated conductor when an external field is applied the charges rearrange themselves end field inside conductor becomes zero. But when this conductor is connected to a battery then charges are not able to accumulate and current flows through the conductor. So, I concluded that internal field is not able to develop and the electric field inside the conductor is solely due to external factors. Now, while studying current electricity I came across this problem that Electric field changes on changing the area of wire. I can understand it using the equations i=j.A and j=E/ρ. But this challenges my previous notions. Where am I going wrong ?

Edit: Perhaps I am skipping the fact that electrons themselves also produce electric field and there would be more electron per unit volume passing through the narrower area(A1). So, they might increase the electric field. Is this the correct explanation?

## 1 Answer

I don't see a contradiction. A power supply takes electrons from one end of a conductor and put them into the other. This separation of charge puts an electric field into the conductor. The field moves electrons down the wire. The strength of the field at any point depends on the gradient of the charge density. If the cross section increases, the current density and field get smaller, but the total current must be constant.