Problem set 07

Problem 1

A current pulse $i_1(t)$ passes through a long thin straight ideal conductor.

The pulse can be described using the Heaviside unit step function $\theta$ as

$$i_1(t) = I_1\:\theta(t)\theta(T-t),$$

where $T$ is the length of the square pulse starting at $t = 0$. Assume the self-inductance of the square conductor to be $L$.

(a) Find the mutual inductance $L_{12}$ and the induced current $i_2(t)$ in the square loop.

(b) If $T >> L/R$ what is the energy dissipated in the resistor $R$?

(c) Through the use of graphics find the limiting form for the induced current $i_2(t)$ when the pulse in the straight conductor gets shorter and shorter and $T << L/R$. Please, scale the equation for $i_2(t)$ in order to use dimensionless quantities in the graphics.

The problem is due Monday March 03 2025 at 20:00