If $n$ represents the actual number of deflections in a converted galvanometer of resistance $G$ and shunt resistance $S$. Then the total current $I$ when its figure of merit is $K$ will be

A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is 

Two long parallel conductors $S_1$ and $S_2$ are separated by a distance $10 \mathrm{cm}$ and carrying currents of $4 \mathrm{A}$ and $2 \mathrm{A}$ respectively. The conductors are placed along $x$-axis in $X-Y$ plane. There is a point $P$ located between the conductors (as shown in figure).
A charge particle of $3\pi$ coulomb is passing through the point $P$ with velocity $\overrightarrow{v}=\left(2\hat{i}+3\hat{j}\right) \mathrm{m} {\mathrm{s}}^{-1}$; where $\hat{i}$ & $\hat{j}$ represents unit vector along $x$ & $y$ axis respectively. The force acting on the charge particle is $4\pi \times {10}^{-5}\left(-x\hat{\mathrm{i}}+2\hat{\mathrm{j}}\right) \mathrm{N}$. The value of $x$ is 

An infinitely long hollow conducting cylinder with radius $R$ carries a uniform current along its surface.

Choose the correct representation of magnetic field $\left(B\right)$as a function of radial distance $\left(r\right)$ from the axis of cylinder.