If an electric current of $4 \pi \sqrt{3}$ A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x \times 10^{-7} \mathrm{~T}$.
The value of $x$ is _________.
Two circular coils $$P$$ and $$Q$$ of 100 turns each have same radius of $$\pi \mathrm{~cm}$$. The currents in $$P$$ and $$R$$ are $$1 A$$ and $$2 A$$ respectively. $$P$$ and $$Q$$ are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is $$\sqrt{x} ~m T$$, where $$x=$$ __________.
[Use $$\mu_0=4 \pi \times 10^{-7} \mathrm{~TmA}^{-1}$$]
An electron moves through a uniform magnetic field $$\vec{B}=B_0 \hat{i}+2 B_0 \hat{j} T$$. At a particular instant of time, the velocity of electron is $$\vec{u}=3 \hat{i}+5 \hat{j} \mathrm{~m} / \mathrm{s}$$. If the magnetic force acting on electron is $$\vec{F}=5 e \hat{k} N$$, where $$e$$ is the charge of electron, then the value of $$B_0$$ is _________ $$T$$.
The current of $$5 \mathrm{~A}$$ flows in a square loop of sides $$1 \mathrm{~m}$$ is placed in air. The magnetic field at the centre of the loop is $$X \sqrt{2} \times 10^{-7} T$$. The value of $$X$$ is _________.