The mean thickness and variance of silicon steel laminations are 0.2 mm and 0.02 respectively. The varnish insulation is applied on both the sides of the laminations. The mean thickness of one side insulation and its variance are 0.1 mm and 0.01 respectively. If the transformer core is made using 100 such varnish coated laminations, the mean thickness and variance of the core respectively are

In a synchronous machine, hunting is predominantly damped by

A hollow metallic sphere of radius r is kept at potential of 1 Volt. The total electric flux coming out of the concentric spherical surface of radius R(>r) is

A perfectly conducting metal plate is placed in x-y plane in a right handed coordinate system. A charge of $$+32{\mathrm{πε}}_0\sqrt2$$ columbs is placed at coordinate (0, 0, 2). $${\mathrm\varepsilon}_0$$ is the permittivity of free space. Assume $$\widehat i,\;\widehat j,\;\widehat k$$ to be unit vectors along x, y and z axes respectively. At the coordinate $$\left(\sqrt2,\sqrt2,0\right)$$, the electric field vector $$\overrightarrow E$$ (Newtons/Columb) will be