All Problems

Electromagnetic Induction. Maxwells Equations

Problem 3.318

Calculate the time constant \(\tau\) of a straight solenoid of length \(l=1.0 \mathrm{~m}\) having a single-layer winding of copper wire whose total mass is equal to \(m=1.0\) kg. The cross-sectional diameter of the solenoid is assumed to be considerably less than its length.

Note. The time constant \(\tau\) is the ratio \(L / R,\) where \(L\) is inductance and \(R\) is active resistance.

Reveal Answer
τ=μ04πmlρρ0=0.7 ms\tau=\frac{\mu_{0}}{4 \pi} \frac{m}{l \rho \rho_{0}}=0.7 \mathrm{~ms}