Seventy-one turns of insulated wire 0.100 cm in diameter are tightly wound to fo

Question

Seventy-one turns of insulated wire 0.100 cm in diameter are tightly wound to form a flat spiral. The spiral fills a disk surrounding a circle of radius 5.00 cm and extending to a radius 12.10 cm at the outer edge. Assume the wire carries a current I at the center of its cross section. Approximate each turn of wire as a circle. Then a loop of current exists at radius 5.05 cm, another at 5.15 cm, and so on. Numerically calculate the magnetic field at the center of the coil. (Assume B is in teslas and Iis in amperes.)

Explanation / Answer

Here , B = summation u0 i / 2r

= 2pi*10^-7* i*[1/0.0505 + 1/0.0515+...]

= 2pi*10^-7* i*100[1/5.05 + 1/5.15+1/5.25+1/5.35+1/...]

total current = 71i, current through thin element at disrance r = i*dr/(0.001)

dB =  2pi*10^-7* [i*dr/(0.001)] 1/r

integral dB = 2pi*10^-7* [i/(0.001)] integral dr/r

B =  2pi*10^-7* [i/(0.001)] ln(12.05/5.05)

B = 2pi*10^-4 i *0.8697

B = 0.0005464 i

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