Chapter 30 Problem 30

Problem

Two tightly wound solenoids have the same length and circular cross-sectional area. But solenoid 1 uses wire that is 1.5 times as thick as solenoid 2.

(a) What is the ratio of their inductances?

(b) What is the ratio of their inductive time constants (assuming no other resistance in the circuits)?

Solution

The magnetic field inside a solenoid (ignoring end effects) is constant: $B=m_{0}nI$ where $n=N/l$. The flux is $\Phi _{B}=BA=m_{0}NIA/l$, so

<math>L=\frac{N\Phi_B}{I}=\frac{m_0 N^2IA}{l}