The torque-speed characteristics of motor ($$T_M$$) and load ($$T_L$$) for two cases are shown in the figures (a) and (b). The load torque is equal to motor torque at points P, Q, R and S The stable operating points 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