A particle having a charge $$100 \mathrm{e}$$ is revolving in a circular path of radius $$0.8 \mathrm{~m}$$ with 1. r.p.s The magnetic field produced at the centre of the circle in SI unit is $$\left(\mu_0=\right.$$ permeability of vacuum, $$e= \left.1.6 \times 10^{-19} \mathrm{C}\right)$$

The magnetic field inside a current carrying toroidal solenoid is $$0.2 \mathrm{~mT}$$. What is the magnetic field inside the toroid if the current through it is tripled and radius is made $$\frac{1}{3}^{\text {rd}}$$ ?

When a battery is connected to the two ends of a diagonal of a square conductor frame of side '$$a$$', the magnitude of magnetic field at the centre will be ( $$\mu_0=$$ permeability of free space)

Two concentric coplanar circular loops of radii '$$r{ }_1$$' and '$$r_2$$' respectively carry currents '$$i_1$$' and '$$\mathrm{i}_2$$' in opposite directions (one clockwise and other anticlockwise). The magnetic induction at the centre of the loops is half that due to '$$i_1$$' alone at the centre. If $$r_2=2 r_1$$, the value of $$\frac{i_2}{i_1}$$