Charge accelerates at bends of the wire?

[gmish27]

charge accelerates at bends of the wire?

hello! can anyone make me understand why and how charge gets accelerated near the bends of wire?

 

[RedX]

It follows from Gauss's law.

Say you have a long, horizontal wire of uniform width, with current flowing from left to right. Draw a box in the wire. The flux through the box is zero, since the electric field is constant in the wire (which is why there is a constant current). Now suppose there is a bend in the wire, say 90 degrees downwards. Draw a Gaussian pillbox at the outside corner of the bend that goes through the upper surface of the horizontal wire. Now in order to maintain a constant current, the electric field must have the same magnitude everywhere in the wire, and must always point in the same direction as the wire. So through the pillbox, there is a flux downwards since current is going down through the bend. There is no flux through the left or right sides, since the pillbox has small walls in those directions. So the only way that the total flux is zero is if electric field comes through the top of the pillbox. But where would this electric field come from? So one is forced to conclude that there is charge on the top surface near the bend, most likely a positive charge.

So basically surface charges near the bends of wire accelerate the charge.

You can plug in numbers yourself. You'll find that for each amp of current that flows through a copper wire, there is about one electron's worth of charge at the bend, so it doesn't much to cause the current to bend.

 

[gmish27]

thnx for the clarification