Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A piece of wire m long carries A. First it is bent into one circle. Find the field at the centre. Then the same wire is bent into equal circles, which lie on top of each other. Find the new field at the centre, and how many times larger it is.
A short piece of current makes , with . A very long wire gives . An arc of angle gives at its centre, and full turns give .
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. Length m, A.
Step 1. One circle. m, so m. Then , that is .
Step 2. Three circles. Now m, so m. Then , that is .
Step 3. The ratio. .
Answer: , , and times.
Watch out. Three times the turns gives three times the field. Each turn is also three times smaller, which gives another factor . So grows as for a fixed length of wire.
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