Electrical – Determining magnetic flux density of a closely wound toroidal coil

electromagneticelectromagnetismmagnetic fluxmagneticsphysics

I am using David K. Chengs's Fundamentals of Engineering Electromagnetics book. In chapter 5/question 5.2, there is a given closely wound toroidal coil, and it asks what is the magnetic flux density at the inside.

This question is okay but at the end it says;

"It is apparent B=0 for r<(b-a) and r>(b+a) since the net total current enclosed by a contour constructed in these two regions is zero."

I understand, at r<(b-a) region, there is no current therefore B=0, but I did not understand the other part which is r>(b+a) how total net current is zero here?

Please see the picture of a question to understand better.

Same question, different edition book

Solution

Best Answer

For r<(b-a), there is no current therefore B=0 (as you already mentioned.)

For r>(b+a), you have to sum up the currents according to their direction. The number of currents/wires pointing into the plot plane is equal to the number of currents pointing out of the surface. The total current is therfore zero.

Related Topic