A charged particle in a uniform magnetic field $$\vec{B}=B_{0} \hat{k}$$ starts moving from the origin with velocity $$v=3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}} ~\mathrm{m} / \mathrm{s}$$. The trajectory of the particle and the time $$t$$ at which it reaches $$2 \mathrm{~m}$$ above $$\mathrm{x}-\mathrm{y}$$ plane are,

A circular coil is placed near a current carrying conductor, both lying on the plane of the paper. The current is flowing through the conductor in such a way that the induced current in the loop is clockwise as shown in the figure. The current in the wire is,

In a closed circuit there is only a coil of inductance L and resistance 100 $$\Omega$$. The coil is situated in a uniform magnetic field. All on a sudden, the magnetic flux linked with the circuit changes by 5 Weber. What amount of charge will flow in the circuit as a result?

$$ \overrightarrow{E} = 90\sin (0.5 \times {10^3}x + 1.5 \times {10^{11}}t)\widehat k$$ V/m. The corresponding magnetic field B will be