A circular coil of radius '$$r$$' and number of turns ' $n$ ' carries a current '$$I$$'. The magnetic fields at a small distance '$$h$$' along the axis of the coil $$\left(B_a\right)$$ and at the centre of the coil $$\left(\mathrm{B}_{\mathrm{c}}\right)$$ are measured. The relation between $$B_c$$ and $$B_a$$ is

A spherical surface of radius of curvature '$$R$$' separates air from glass of refractive index 1.5. The centre of curvature is in the glass. A point object $$\mathrm{P}$$ placed in air forms a real image $$\mathrm{Q}$$ in the glass. The line $$P Q$$ cuts the surface at point '$$O$$' and $$\mathrm{PO}=\mathrm{OQ}=\mathrm{x}$$. Hence the distance '$$\mathrm{x}$$' is equal to

The rotational kinetic energy and translational kinetic energy of a rolling body are same, the body is

Two concentric circular coils A and B have radii $$20 \mathrm{~cm}$$ and $$10 \mathrm{~cm}$$ respectively lie in the same plane. The current in coil A is $$0.5 \mathrm{~A}$$ in anticlockwise direction. The current in coil B so that net field at the common centre is zero, is