A particle of charge $q$ and mass $m$ starts moving form the origin under the action of an electric field $\overrightarrow{E}=E_0\widehat{\mathrm{i}}$ and $\overrightarrow{B}=B_0\widehat{\mathrm{i}}$ with velocity $\overrightarrow{v}=v_0\widehat{\mathrm{j}}$. The speed of the particle will become $2v_0$ after a time.

(1) The magnetic field strength may have been increased while the particle was travelling in air
(2) The particle lost energy by ionising the air
(3) The particle lost charge by ionising the air

A negative charge is given to a nonconducting loop and the loop is rotated in the plane of paper about its centre as shown in figure. The magnetic field produced by the ring affects a small magnet placed above the ring in the same plane :

A current element $∆\overrightarrow{l}=∆x\hat{i}-∆y\hat{j}$ carries $10\mathrm{A}$ current. It is placed at origin. Magnitude of magnetic field at point '$P$' which is at position vector $\overrightarrow{r}=\left(\hat{i}+\hat{j}\right)m$ with respect to origin is $B$ (where $∆x=∆y=1\mathrm{mm}$). 

Find $B\times {10}^{10}$ (In SI units).

A pair of stationary and infinitely long bent wires are placed in the $x-y$ plane as shown in the figure. The wires carry currents of $i=10 \mathrm{A}$ each as shown. The segments $L$ and $M$ are along the $x$-axis. The segment $P$ and $Q$ are parallel to the $y$-axis such that $OS=OR=0.02 \mathrm{m}$. Final value of, $B\times {10}^4$, where $B$ is the magnitude of the magnetic induction at the origin $O$ (in SI units)