The magnetic field at the centre of a circular coil of radius '$$R$$', carrying current $$2 A$$ is '$$B_1$$'. The magnetic field at the centre of another coil of radius '$$3 R$$' carrying current $$4 A$$ is '$$B_2$$'. The ratio $$B_1:B_2$$ is

Two wires $$2 \mathrm{~mm}$$ apart supply current to a $$100 \mathrm{~V}, 1 \mathrm{~kW}$$ heater. The force per metre between the wires is ( $$\mu_0=4 \pi \times 10^{-27}$$ SI unit)

Two long parallel wires carrying currents $$8 \mathrm{~A}$$ and $$15 \mathrm{~A}$$ in opposite directions are placed at a distance of $$7 \mathrm{~cm}$$ from each other. A point '$$\mathrm{P}$$' is at equidistant from both the wires such that the lines joining the point to the wires are perpendicular to each other. The magnitude of magnetic field at point '$$\mathrm{P}$$' is $$(\sqrt{2}=1.4) ( \mu_0=4 \pi \times 10^{-7}$$ SI units)

Electron of mass '$$\mathrm{m}$$' and charge '$$\mathrm{q}$$' is travelling with speed '$$v$$' along a circular path of radius '$$R$$', at right angles to a uniform magnetic field of intensity '$$B$$'. If the speed of the electron is halved and the magnetic field is doubled, the resulting path would have radius