Current $I$ is carried in a wire of length ' $L$ '. If wire is bent into a circular coil of single turn, the maximum torque in a given magnetic field $B$ is

A square of side ' $L$ ' metre lies in $x-y$ plane in a region where the magnetic field is $\overline{\mathrm{B}}$ and $\vec{B}=B_0(2 \hat{i}+3 \hat{j}+4 \hat{k})$, where $B_0$ is constant. The magnitude of flux passing through the square (in weber) is

A long straight wire of radius ' $r$ ' carries a steady current ' $I$ '. The current is uniformly distributed over its cross-section. The ratio $\left(\frac{B}{B_1}\right)$ of the magnetic field ' B ' and ' $\mathrm{B}_1$ ' at radial distances ' $\frac{r}{2}$ ' and ' $3 r$ respectively, from the axis of the wire is

In hydrogen atom, an electron of charge 'e' revolves in an orbit of radius ' $r$ ' with speed ' $v$ '. The magnetic moment associated with electron is