= Solution
Assume that the transverse field is large enough to saturate through the thickness despite demagnetizing effects, and retain the thin-layer plane-stress and open-circuit assumptions from part(a). The two imposed in-plane strains now become
$$
\varepsilon_x=\varepsilon_y=-\Lambda/2=2\times10^{-5}.
$$
Their sum is $-\Lambda$, whereas it was $\Lambda/2$ for longitudinal saturation. The in-plane <stress> sum, and hence the induced open-circuit <voltage>, is multiplied by $-2$:
$$
\boxed{V_{\rm thickness}\simeq-2V_{\rm longitudinal}.}
$$
Thus \b[the magnitude is about $24\,\mathrm{mV}$ with the opposite polarity], under this model. The larger demagnetizing field for an out-of-plane direction means the same external field magnitude might not produce the same degree of saturation. Changes in thickness constraint or <strain> transfer would also modify the estimate.
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