To construct a solenoid, you wrap insulated wire uniformly around a plastic tube 7.1 cm in diameter and 57 cm in length. You would like a 3.0 A current to produce a 2.6 kG magnetic field inside your solenoid. What is the total length of wire you will need to meet these specifications?

We need about 8769 meters of wire to produce a 2.6 kilogauss magnetic field.

Explanation:

Recall the formula for the magnetic field produced by a solenoid of length L. N turns, and running a current I:

So, in our case, where B = 2.6 KG = 0.26 Tesla; I is 3 amperes, and L = 0.57 m, we can find what is the number of turns needed;

Therefore we need about 39312 turns of wire. Considering that each turn must have a length of , where D is the diameter of the plastic cylindrical tube, then the total length of the wire must be:

We can round it to about 8769 meters.

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