Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A long straight cable under a floor carries a steady current of A. What is the magnetic field at a distance of cm from it? At what distance is the field ?
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. A, m, .
Step 1. The field at cm. , that is .
Step 2. The distance for . We want , so m, that is cm.
Answer: , and cm.
Check. The field falls as . The new distance is times the first, and the field is a third of , which is . It fits.
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