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Chapter 27: Problem 7

You have a fixed length of wire to wind into an inductor. Will you get more inductance if you wind a short coil with large diameter, or a long coil with small diameter?

Short Answer

Expert verified
You would get more inductance by winding a long coil with a small diameter.

Step by step solution

01

Understanding the Problem

The problem involves determining which shape of coil (short and thick vs. long and thin) will offer greater inductance when using a fixed length of wire. The length of the coil \(l\) and the cross-sectional area \(A\) are the aspects of the coil's geometry that can be adjusted.
02

Analysis of the formula

According to the formula of inductance, an increase in the cross-sectional area \(A\) or decrease in length \(l\) results in an increase in inductance \(L\). Thus, a coil with a larger diameter (larger \(A\)) and smaller length (shorter \(l\)) will have higher inductance. It's important to note that the length of wire is fixed, which means that the number of turns \(N\) is also inversely proportional to \(A\). As \(A\) increases, \(N\) decreases.
03

Final conclusion

Though a larger \(A\) and smaller \(l\) increases \(L\), the reduction in \(N\) as \(A\) increases counters this. In fact, since the number of turns \(N\) appears squared in the formula, it has a greater influence on \(L\). Therefore, one would get more inductance by winding a long coil with a small diameter (more turns \(N\), smaller \(A\), and longer \(l\)).

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Most popular questions from this chapter

A uniform magnetic field is given by \(\vec{B}=b t \hat{k},\) where \(b=\) 0.35 T/s. Find the induced current in a conducting loop with area \(240 \mathrm{cm}^{2}\) and resistance \(0.20 \Omega\) that lies in the \(x-y\) plane. In what direction is the current, as viewed from the positive z-axis?

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