$A$ rod $AB$ moves with a uniform velocity $v$ in a uniform magnetic field as shown in the figure.

$A$ charged particle of $2\,\mu\,C$ accelerated by a potential difference of $100\,V$ enters a region of uniform magnetic field of magnitude $4\,mT$ at a right angle to the direction of the field. The charged particle completes a semicircle of radius $3\,cm$ inside the magnetic field. The mass of the charged particle is $........\times 10^{-18}\,kg$.

An electron is projected normally from the surface of a sphere of radius $a$ with speed $v_0$ into a uniform magnetic field $B$ perpendicular to the plane of the paper. The centre of the sphere is at a distance $b$ from a wall. If the electron strikes the wall tangentially,what should be the magnetic field $B$?

An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the $+x$ direction and a magnetic field along the $+z$ direction,then

An $\alpha$-particle of mass $m$ moves on a circular path of radius $r$ in a plane inside and normal to a uniform magnetic field $B$. The time taken by this particle to complete one revolution is . . . . . . .

$A$ deuteron of kinetic energy $50 \, keV$ is describing a circular orbit of radius $0.5 \, m$ in a plane perpendicular to a magnetic field $\vec{B}$. The kinetic energy of a proton that describes a circular orbit of radius $0.5 \, m$ in the same plane with the same $\vec{B}$ is ........ $keV$.