Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
The core of a transformer is built from silicon steel sheets mm thick. The resistivity of the steel is . The peak field in the core is T, at Hz, and the core has a volume of . Find the eddy-current loss in each cubic metre and in the whole core. Then find the loss in the whole core if the sheets were mm thick.
A changing flux drives eddy currents in a solid conductor. They oppose the change (Lenz's law), so a moving conductor is braked, and the work done becomes heat. At a steady speed, the drag equals the weight in a fall, , and the heat each second is . A disc of radius and thickness in a field changing at loses . In a thin sheet, .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. m, T, Hz, , .
Step 1. The loss in each cubic metre. .
Step 2. The whole core. .
Step 3. Thicker sheets. The loss goes as . Twice the thickness gives times the loss: .
Answer: , W and W.
Check. The loss in each cubic metre is a few kilowatts, the size that real cores show. The loss is small because the sheets are thin.
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