If in a circular coil $$A$$ of radius $$R,$$ current $$I$$ is flowing and in another coil $$B$$ of radius $$2R$$ a current $$2I$$ is flowing, then the ratio of the magnetic fields $${B_A}$$ and $${B_B}$$, produced by them will be

The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its

Wires $$1$$ and $$2$$ carrying currents $$i{}_1$$ and $$i{}_2$$ respectively are inclined at an angle $$\theta $$ to each other. What is the force on a small element $$dl$$ of wire $$2$$ at a distance of $$r$$ from wire $$1$$ (as shown in figure) due to the magnetic field of wire $$1$$?

The power factor of $$AC$$ circuit having resistance $$(R)$$ and inductance $$(L)$$ connected in series and an angular velocity $$\omega $$ is