Two similar coils $A$ and $B$ of radius '$$r$$' and number of turns '$$N$$' each are placed concentrically with their planes perpendicular to each other. If I and $$2 \mathrm{I}$$ are the respective currents passing through the coils then the net magnetic induction at the centre of the coils will be:

A circular coil of radius $$0.1 \mathrm{~m}$$ is placed in the $$\mathrm{X}-\mathrm{Y}$$ plane and a current $$2 \mathrm{~A}$$ is passed through the coil in the clockwise direction when looking from above. Find the magnetic dipole moment of the current loop

Two circular coils of radius '$$a$$' and '$$2 a$$' are placed coaxially at a distance ' $$x$$ and '$$2 x$$' respectively from the origin along the $$\mathrm{X}$$-axis. If their planes are parallel to each other and perpendicular to the $$\mathrm{X}$$ - axis and both carry the same current in the same direction, then the ratio of the magnetic field induction at the origin due to the smaller coil to that of the bigger one is:

Two very long straight parallel wires carry currents $$i$$ and $$2 i$$ in opposite directions. The distance between the wires is $$r$$. At a certain instant of time a point charge $$q$$ is at. a point equidistant from the two wires in the plane of the wires. Its instantaneous velocity $$v$$ is perpendicular to this plane. The magnitude of the force due to the magnetic field acting on the charge at this instant is