The relay circuit shown in Eigure P14.32 has the following parameters: $A_{\text {gap }}= 0.001 \mathrm{~m}^2 ; N=500$ turns; $L=0.02 \mathrm{~m} ; \mu=\mu_0=4 \pi \times 10^{-7}$ (neglect the iron reluctance); $k=1,000 \mathrm{~N} / \mathrm{m} ; R=18 \Omega$. What is the minimum DC supply voltage υ for which the relay will make contact when the electrical switch is
closed?