Axis of a solid cylinder of infinite length and radius $R$ lies along the $y-$axis. It carries a uniformly distributed current $i$ along $+y$ direction. Magnetic field at a point $\left(\frac{R}{2}, y, \frac{{\displaystyle R}}{{\displaystyle 2}}\right)$ is 

A uniform magnetic field, $\overrightarrow{B}=\left(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}+\hat{\mathrm{k}}\right) \mathrm{T}$  exists in region of space. A semicircular wire of radius $1 \mathrm{m}$ carrying current $1 \mathrm{A}$ having its centre at $(2, 2, 0)$ is placed in $x-y$ plane as shown in fig. The force on semicircular wire will be

Which of the following statement is correct in the given figure.

A magnetic field $\overrightarrow{B}=B_0\hat{\mathrm{j}}$ exists in the region $\mathrm{a}<\mathrm{x}<2\mathrm{a}$ and $\overrightarrow{B}=-B_0\hat{\mathrm{j}},$ in the region $2a<x<3a,$ where $B_0$ is a positive constant. A positive point charge moving with a velocity $\overrightarrow{V}=v_0\hat{\mathrm{i}},$ where $v_0$ is a positive constant, enters the magnetic field at $x=a .$ The trajectory of the charge in this region can be like.

A conductor (shown in the figure) carrying contant current $\mathrm{I}$ is kept in the $x-y$ plane in a uniform magnetic field $\overrightarrow{B}.$ IF $F$ is the magnitude of the total magnetic force acting on the conductor, then the incorrect statement is: