Thirty-seven turns of insulated wire 0.100 cm in diameter are tightly wound to f

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

Explanation / Answer

Solution:

Each turn creates a field at the center

B=uoI/2R

Therefore total magnetic field is

B=(uoI/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

Please Rate, Ask Your Query in comment Box. Thank You :)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.