E10B8 - Magnetic Field as the Center of a Current Loop with Many Windings Imagin

Question

E10B8 - Magnetic Field as the Center of a Current Loop with Many Windings Imagine Winding N turns of wire in a circular loop of radius R. Each turn in this coil acts like a loop of radius R, so the magnetic field at the coil's center is N times larger than that for a single loop of the same size. If the wire can safely carry 1.0 A of current, how many turns would you need to produce a magnetic field of 1.0 mT (20 in diameter? at the center of a coil 22 cm The number of turns needed to produce a magnetic field of 1.0 mT is

Explanation / Answer

Magnetic field at the center of the loop = (uo*N*i)/2R

Given ,
i = 1.0 A
B = 1.0 mT
D = 2R = 22 cm = 0.22 m

Substituing values,
1.0 * 10^-3 = (4 * 10^-7 * 1.0 * N)/0.22
N = 175

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