Two points $A$ and $B$ on the axis of a circular current loop are at distances of 4 cm and $3 \sqrt{3} \mathrm{~cm}$ from the centre of the loop. If the ratio of the induced magnetic fields at points $A$ and $B$ is $216: 125$, then radius of the loop is

Two charged particles $A$ and $B$ of masses $m$ and $2 m$, charges $2 q$ and $3 q$ respectively moving with same velocity enter a uniform magnetic field such that both the particles make same angle ( $<90^{\circ}$ ) with the direction of the magnetic field. Then, the ratio of pitches of the helical paths of the particles $A$ and $B$ is

A particle of charge 2 C is moving with a velocity of $(3 \hat{\mathbf{i}}+4 \hat{\mathrm{j}}) \mathrm{ms}^{-1}$ in the presence of magnetic and electric fields. If the magnetic field is $(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \mathrm{T}$ and the electric field is $(-2 \hat{\mathbf{k}}) \mathrm{NC}^{-1}$, then the Lorentz force on the particle is

A rectangular coil of 400 turns and $10^{-2} \mathrm{~m}^2$ area, carrying a current of 0.5 A is placed in a uniform magnetic field of IT such that the plane of the coil makes an angle of $60^{\circ}$ with the direction of the magnetic field. The initial moment of force acting on the coil in $\mathrm{N}-\mathrm{m}$ is