4.2.10 Problems and solutions

The problems of this subsection use the tools of the section in the order in which they were introduced: the force $F=\oint Idl\times B$ of one current on another, Ampère's law $\oint H\cdot dl=I_{\text{enc}}$ with $B=\mu H$, the inductances $L_{12}=N_2{\Phi }_{12}/I_1$ and $L_{11}=N_1{\Phi }_{11}/I_1$, the energy $W_m=\frac{1}{2}\int H\cdot BdV=\frac{1}{2}L{I}^2$, Ohm's law $J=\sigma E$ with the Joule power $p=J\cdot E$, and the dipole $m=IS{a}_n$ with its torque $T=m\times B$. The constants used are ${\mu }_0=4\pi \times 10^{-7}=1.2566\times 10^{-6}H/m$ and $g=9.81m/{\mathrm{s}}^2$.