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

A straight wire of length $$2 \mathrm{~m}$$ carries a current of $$10 \mathrm{~A}$$. If this wire is placed in uniform magnetic field of $$0.15 \mathrm{~T}$$ making an angle of $$45^{\circ}$$ with the magnetic field, the applied force on the wire will be

A square wire of each side l carries a current $$I$$. The magnetic field at the mid-point of the square