A cyclotron is used to accelerate protons. If the operating magnetic field is $$1.0 \mathrm{~T}$$ and the radius of the cyclotron 'dees' is $$60 \mathrm{~cm}$$, the kinetic energy of the accelerated protons in MeV will be :

$$[\mathrm{use} \,\,\mathrm{m}_{\mathrm{p}}=1.6 \times 10^{-27} \mathrm{~kg}, \mathrm{e}=1.6 \times 10^{-19} \,\mathrm{C}$$ ]

Two concentric circular loops of radii $$r_{1}=30 \mathrm{~cm}$$ and $$r_{2}=50 \mathrm{~cm}$$ are placed in $$\mathrm{X}-\mathrm{Y}$$ plane as shown in the figure. A current $$I=7 \mathrm{~A}$$ is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately :

A charge particle is moving in a uniform magnetic field $$(2 \hat{i}+3 \hat{j}) \,\mathrm{T}$$. If it has an acceleration of $$(\alpha \hat{i}-4 \hat{j})\, \mathrm{m} / \mathrm{s}^{2}$$, then the value of $$\alpha$$ will be :

$$\mathrm{B}_{X}$$ and $$\mathrm{B}_{\mathrm{Y}}$$ are the magnetic fields at the centre of two coils $$\mathrm{X}$$ and $$\mathrm{Y}$$ respectively each carrying equal current. If coil $$X$$ has 200 turns and $$20 \mathrm{~cm}$$ radius and coil $$Y$$ has 400 turns and $$20 \mathrm{~cm}$$ radius, the ratio of $$B_{X}$$ and $$B_{Y}$$ is :