All Problems

Electromagnetic Induction. Maxwells Equations

Problem 3.318

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

Note. The time constant τ\tau is the ratio L/R,L / R, where LL is inductance and RR 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}