All Problems

Constant Magnetic Field, Magnetics

Problem 3.238

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

Reveal Answer
B={(μ0I/h)(1(h/2πR)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.