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 $$\frac{i_2}{i_1}$$

The Kirchhoff's current law and voltage law are respectively based upon the conservation of

The permeability of a metal is $$0.1256 ~\mathrm{TmA}^{-1}$$. Its relative permeability will be $$\mathrm{\left( {{{{\mu _0}} \over {4\pi }} = {{10}^{ - 7}}\,SI\,unit} \right)}$$ ($$\pi=3.14$$)

The angular displacement of body performing circular motion is given by $$\theta=5 \sin \frac{\pi t}{6}$$. The angular velocity of the body at $$t=3$$ second will be $$\left[\sin \frac{\pi}{2}=1, \cos \frac{\pi}{2}=0\right]$$