An alternator with an internal voltage of $1 \delta_1$ pu and synchronous reactance of 0.4 pu is connected by a transmission line of reactance 0.1 pu to a synchronous motor having synchronous reactance 0.35 pu and internal voltage of $0.85 \delta_2 \mathrm{pu}$. If the real power supplied by the alternator is 0.866 pu , then ( $\delta_1-\delta_2$ ) is $\_\_\_\_$ degrees (Round off to 2 decimal places). (Machines are of non-salient type. Neglect resistances)

Which one of the following vector functions represents a magnetic field $\vec{B}$ ? ( $\hat{x}, \hat{y}$, and $\hat{z}$ are unit vectors along $x$-axis, $y$-axis and $z$-axis respectively)

A $1 \mu \mathrm{C}$ point charge is held at the origin of a cartesian coordinate system. If a second point charge of $10 \mu \mathrm{C}$ is moved from $(0,10,0)$ to $(5,5,5)$ and subsequently to $(5,0,0)$, then the total work done is

$\_\_\_\_$ mJ . (Round off to 2 decimal places). Take $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9$ in SI units. All coordinates are in meters.

One Coulomb of point charge moving with a uniform velocity $10 \hat{x} \mathrm{~m} / \mathrm{s}$ enters the region $x \geq 0$ having a magnetic flux density $\vec{B}=(10 y \hat{x}+10 x \hat{y}+10 \hat{z}) \mathrm{T}$. The magnitude of force on the charge at $x=0^{+}$is

$\_\_\_\_$ N. ( $\hat{x}, \hat{y}$ and $\hat{z}$ are unit vectors along x -axis, y -axis and z -axis respectively)