A particle of charge $Q$ and mass $m$ is initially at rest at origin. Electric field is given by $E_0 \hat{j}$ while magnetic field is $B_0\hat{k}.$ Find speed of particle when the coordinator of particle are $\left(\frac{2\pi mv}{qB}, 0, 0\right).$

Find magnetic moment in following cases.

Magnetic field in a region is given by $\overrightarrow{\mathrm{B}}={\mathrm{B}}_0\hat{\mathrm{i}}+2{\mathrm{B}}_0 \hat{\mathrm{j}}.$ Find torque on the loop shown in figure.

A magnetic dipole is placed as shown in figure. Find work done by external agent in rotating it by $90°$ anticlockwise and clockwise.

A current carrying loop is placed in magnetic field as shown in figure. Find time period of small oscillation around as axis passing through diameter of coil. Mass of coil is $\mathrm{m},$ radius is $\mathrm{R}.$