Question 706747: You can make an electromagnet by wrapping a wire around a nail and then sending a current through the wire.The strength of the magnet is directly proportional to the number of wrappings. The nail, (pictured in Homework Paper, has a diameter of 0.4 Cm). The wire is 0.05 cm in diameter, and you can get a 100 wrappings side-by-side on the nail before having to start another layer. Consider each wrapping a perfect circle. How many meters of wire do you need to the nearest 0.1 m, to make a magnet with 700 wrappings?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Considering each wrapping a perfect circle, the first 100 wrappings would be 100 circles of radius 0.2 cm, diameter 0.4 cm.
(I'm counting the radius as going from the very center of the nail to the surface where the nail touches the wire, not the slightly larger diameter to the very center of the wire).
That would account for
 per wrapping or   for the first 100 wrappings.
The next 100 wrappings are wrapped around nail plus one layer of wire, with a radius of  and a radius of 
The total length of wire for that second layer would be
 .
The third layer would be wrapped around the nail plus two layers of wire with a new, larger diameter of  and would total  of wire.
The length of wire for each layer keeps increasing, and the total length of wire for the 7 layers, meaning 700 wrappings, on diameters measuring, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 cm is
That is  .
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