The magnetic flux linked with a coil is given by the equation: $$\phi=8 t^2+t+10$$. The e.m.f. induced in the coil in the $$3^{\text {rd }}$$ second will be

A wire ' 1 ' $$\mathrm{cm}$$ long bent into a circular loop is placed perpendicular to the magnetic field of flux density '$$B^{\prime} W b \mathrm{~m}^{-2}$$. Within $$0.1 \mathrm{sec}$$, the loop is changed into a square of side '$$a$$' $$\mathrm{cm}$$ and flux density is doubled. The value of e.m.f. induced is

In an inductor of self-inductance $$2 \mathrm{~mH}$$, current changes with time (in sec) according to the relation, $$I=(3 t^2-3 t+8) A$$. The emf becomes zero at

A metallic rod of length '$$a$$' is rotated with an angular frequency of $$0.2 \mathrm{~rads}^{-1}$$ about an axis normal to the rod passing through its one end. A constant and uniform magnetic field of '$$\mathrm{B}$$' T parallel to the axis exists everywhere. The emf developed across the ends of the rod is