The magnetic field at the center of current carrying circular loop is $$B_{1}$$. The magnetic field at a distance of $$\sqrt{3}$$ times radius of the given circular loop from the center on its axis is $$B_{2}$$. The value of $$B_{1} / B_{2}$$ will be

The current sensitivity of a galvanometer can be increased by :

(A) decreasing the number of turns

(B) increasing the magnetic field

(C) decreasing the area of the coil

(D) decreasing the torsional constant of the spring

Choose the most appropriate answer from the options given below :

As shown in the figure, a metallic rod of linear density $$0.45 \mathrm{~kg} \mathrm{~m}^{-1}$$ is lying horizontally on a smooth inclined plane which makes an angle of $$45^{\circ}$$ with the horizontal. The minimum current flowing in the rod required to keep it stationary, when $$0.15 \mathrm{~T}$$ magnetic field is acting on it in the vertical upward direction, will be :

{Use $$g=10 \mathrm{~m} / \mathrm{s}^{2}$$}

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 :

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