A charged particle is moving in a uniform magnetic field in a circular path. Radius of circular path is $R$. When energy of particle is doubled, then new radius will be
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A square frame of side I carries a current $i$. The magnetic field at its centre is $B$. The same current is passed through a circular coil having the same perimeter as the square. The field at the centre of the circular coil is $B^{\prime}$. The ratio of $\frac{B}{B^{\prime}}$ is
A circular coil having $N$ $turns$ is made from a wire of length $L$ $meter$. If a current $I$ $ampere$ is passed through it and is placed in a magnetic field of $B$ $Tesla$, the maximum torque on it is
Two circular coils $P$ and $Q$of $100$ turns each have same radius of $\pi \mathrm{cm}$. The currents in $\mathrm{P}$ and $\mathrm{R}$ are $1 \mathrm{~A}$ and $2 \mathrm{~A}$ respectively. $\mathrm{P}$ and $\mathrm{Q}$ are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is $\sqrt{\mathrm{x}} \mathrm{mT}$, where X=___.
$\left[\text { Use } \mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\right]$
Two charged particle $A$ and $B$ each of charge $+e$ and masses $12$ $amu$ and $13$ $amu$ respectively follow a circular trajectory in chamber $X$ after the velocity selector as shown in the figure. Both particles enter the velocity selector with speed $1.5 \times 10^6 \,ms^{-1}.$ A uniform magnetic field of strength $1.0$ $T$ is maintained within the chamber $X$ and in the velocity selector.