An $\alpha - $ particle travels in a circular path of radius $0.45\, m$ in a magnetic field $B = 1.2\,Wb/{m^2}$ with a speed of $2.6 \times {10^7}\,m/\sec $. The period of revolution of the $\alpha - $ particle is

A magnetic field $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{\mathrm{j}}$ exists in the region $\mathrm{a} < \mathrm{x} < 2 \mathrm{a}$ and $\vec{B}=-B_0 \hat{j}$, in the region $2 \mathrm{a} < \mathrm{x} < 3 \mathrm{a}$, where $\mathrm{B}_0$ is a positive constant. $\mathrm{A}$ positive point charge moving with a velocity $\overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{\dot{i}}$, 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 particle of charge per unit mass $\alpha$ is released from origin with a velocity $\bar{v}=v_0 \vec{i}$ in a uniform magnetic field $\bar{B}=-B_0 \hat{k}$. If the particle passes through $(0, y, 0)$ then $y$ is equal to

A charge of $1\,C$ is moving in a magnetic field of $0.5\,Tesla$ with a velocity of $10\,m/sec$ Perpendicular to the field. Force experienced is.....$N$

Electron of mass $m$ and charge $q$ is travelling with a speed along a circular path of radius $r$ at right angles to a uniform magnetic field of intensity $B$. If the speed of the electron is doubled and the magnetic field is halved the resulting path would have a radius

At $t = 0$ a charge $q$ is at the origin and moving in the $y-$ direction with velocity $\overrightarrow v  = v\,\hat j .$ The charge moves in a magnetic field that is for $y > 0$ out of page and given by $B_1 \hat z$ and for $y < 0$ into the page and given $-B_2 \hat z .$ The charge's subsequent trajectory is shown in the sketch. From this information, we can deduce that