The capacitance of the arrangement shown in Fig. is ................... $$pF$$

A infinitely long straight wire carries $$1000$$ $$A$$ of current and in the vicinity, there is a circular conducting loop of $$100$$ $$mm$$ diameter with the center of the loop $$1$$ $$m$$ away from the straight conductor. Both the wire and the loop are coplanar. Determine the magnitude and direction of current in the loop that produces a zero flux density at its center.

A square coil of $$10$$ turns and $$10$$ $$cm$$ side is moved through a steady magnetic field of $$1$$ $$Wb/{m^2}$$ at a constant velocity of $$2$$ $$m/sec$$ with its plane perpendicular to the field as shown in Fig. Plot the variation of induced $$e.m.f$$ as the coil moves along the field.

Express the given matrix $$A = \left[ {\matrix{ 2 & 1 & 5 \cr 4 & 8 & {13} \cr 6 & {27} & {31} \cr } } \right]$$
as a product of triangular matrices $$L$$ and $$U$$ where the diagonal elements of the lower triangular matrices $$L$$ are unity and $$U$$ is an upper triangular matrix.