Two long conductors, separated by a distance '$$\mathrm{d}$$' carry currents '$$\mathrm{I}_1$$' and '$$\mathrm{I}_2$$' in the same directions. They exert a force '$$\mathrm{F}$$' on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to '$$3 \mathrm{~d}$$'. The new value of the force between them is

An electron in a circular orbit of radius $$0.05 \mathrm{~nm}$$ performs $$10^{14}$$ revolutions/second. What is the magnetic moment due to the rotation of electron? $$(\mathrm{e}=1.6 \times 10^{-19} \mathrm{C})$$

A long solenoid carrying current $$\mathrm{I}_1$$ produces magnetic field $$\mathrm{B}_1$$ along its axis. If the current is reduced to $$20 \%$$ and number of turns per $$\mathrm{cm}$$ are increased five times then new magnetic field B$$_2$$ is equal to

A straight wire of diameter $$0.4 \mathrm{~mm}$$ carrying a current of $$2 \mathrm{~A}$$ is replaced by another wire of 0.8 $$\mathrm{mm}$$ diameter carrying the same current. The magnetic field at distance $$(\mathrm{R})$$ from both the wires is 'B$$_1$$' and 'B$$_2$$' respectively. The relation between B$$_1$$ and B$$_2$$ is