BaTiO$3$ has a piezoelectric strain coefficient, d$33=150$ x $10-12$ C$/$N with a dielectric constant, $33=750$ and an elastic compliance s$33=5$x$10-12$ m$2/$N$.$ Calculate the induced strain under an applied electric field of E$3=10$x$105$ V$/$m$.$ Then calculate the generative stress under a completely clamped condition.

For BaTiO$3$ calculate the induced electric field under an applied stress of X$3=3$x$107$ N$/$m$2.$ The induced field does not coincide with the electric field. Explain the reason taking into account the electromechanical coupling factor, k$.$