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Constant Magnetic Field, Magnetics

Problem 3.238

A thin conducting strip of width h=2.0 cmh=2.0 \mathrm{~cm} is tightly wound in the shape of a very long coil with cross-section radius R=R= =2.5 cm=2.5 \mathrm{~cm} to make a single-layer straight solenoid. A direct current I=5.0I=5.0 A flows through the strip. Find the magnetic induction inside and outside the solenoid as a function of the distance rr from its axis.

Reveal Answer
B={(μ0I/h)(1−(h/2πR⃗)2=0.3 m T,r<R,(μ0/4π)2I/r,r>R.B=\left\{\begin{array}{l} \left.\left(\mu_{0} I / h\right) \sqrt{(1-(h / 2 \pi} \vec{R}\right)^{2}=0.3 \mathrm{~m} \mathrm{~T}, r<R, \\ \left(\mu_{0} / 4 \pi\right) 2 I / r, r>R . \end{array}\right.
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