A parallel plate capacitor consisting two dielectric materials is shown in the figure. The middle dielectric slab is place symmetrically with respect to the plates. If the potential difference between one of the plates and the nearest surface of dielectric interface is 2 Volts, then the ratio $$\varepsilon_1\;:\;\varepsilon_2$$ is

Divergence of the three-dimentional radial vector field $$\overrightarrow F$$ is

Divergence of the vector field $$$\overrightarrow V\left(x,y,z\right)=-\left(x\cos xy\;+\;y\right)\;\widehat i\;+\;\left(y\cos xy\right)\;\widehat j\;+\;\left(\sin\;z^2\;+\;x^2\;+\;y^2\right)\widehat k$$$ is

A parallel plate capacitor is shown in Fig. It is made of two square metal plates of $$400$$ $$mm$$ side. The $$14$$ $$mm$$ space between the plates is filled with two layers of dielectrics of $${\varepsilon _r} = 4,6\,\,mm$$ thick and $${\varepsilon _r} = 2,8\,\,mm$$ thick. Neglecting fringing of fields at the edges, the capacitance is