Question

Thirty-seven 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 8.70 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 I is in amperes.) B = I

Answer 1

Solution:

Each turn creates a field at the center

B=u_oI/2R

Therefore total magnetic field is

B=(u_oI/2)[1/R₁ +1/R₂ +1/R₃+------+1/R₃₇]

B=((4pi*10^-7)*I/2)[1/5.05 +1/5.15 +1/5.25+1/5.35+1/5.45+--------+1/8.55+1/8.65]*10²

B=(2pi*10^-7)I*(5.802)*10²

B=(3.643*10^-4)I

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