There is a ring of radius $r$ having linear charge density $\lambda$ and rotating with a uniform angular velocity $\omega$. The magnitude of the magnetic field produced by this ring at its own centre would be ( $\mu_0=$ permeability of air)

A particle of charge ' $q$ ' and mass ' $m$ ' moves in a circular orbit of radius ' $r$ ' with angular speed ' $\omega$ '. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

A charged particle moving with a velocity $$\vec{v}=v_1 \hat{i}+v_2 \hat{j}$$ in a magnetic field $$\vec{B}$$ experiences a force $$\vec{F}=F_1 \hat{i}+F_2 \hat{j}$$. Here $$v_1, v_2, F_1, F_2$$ all are constants. Then $$\overrightarrow{\mathrm{B}}$$ can be

A wire carrying a steady current I is kept in the x-y plane along the curve $$y=A \sin \left(\frac{2 \pi}{\lambda} x\right)$$. A magnetic field B exists in the z-direction. The magnitude of the magnetic force in the portion of the wire between x = 0 and x = $$\lambda$$ is