A particle of charge $16\times10^{-16}\, C$ moving with velocity $10\, ms^{-1}$ along $x-$ axis enters a region where magnetic field of induction $\vec B$ is along the $y-$ axis and an electric field of magnitude $10^4\, Vm^{-1}$ is along the negative $z-$ axis. If the charged particle continues moving along $x-$ axis, the magnitude of $\vec B$ is

A particle of mass $m$ and charge $\mathrm{q}$, moving with velocity $\mathrm{V}$ enters Region $II$ normal to the boundary as shown in the figure. Region $II$ has a uniform magnetic field B perpendicular to the plane of the paper. The length of the Region $II$ is $\ell$. Choose the correct choice$(s)$.

Figure: $Image$

$(A)$ The particle enters Region $III$ only if its velocity $V>\frac{q / B}{m}$

$(B)$ The particle enters Region $III$ only if its velocity $\mathrm{V}<\frac{\mathrm{q} / \mathrm{B}}{\mathrm{m}}$

$(C)$ Path length of the particle in Region $II$ is maximum when velocity $V=\frac{q / B}{m}$

$(D)$ Time spent in Region $II$ is same for any velocity $V$ as long as the particle returns to Region $I$

When a charged particle moving with velocity $\vec v$ is subjected to a magnetic field of induction $\vec B$, the force on it is non-zero. This implies that

A particle of mass $m$ and charge $q$ is in an electric and magnetic field given by

$\vec E = 2\hat i + 3\hat j ;\, B = 4\hat j + 6\hat k$

The charged particle is shifted from the origin to the point $P(x = 1 ;\, y = 1)$ along a straight path. The magnitude of the total work done is

An electron is moving along $+x$ direction with a velocity of $6 \times 10^{6}\, ms ^{-1}$. It enters a region of uniform electric field of $300 \,V / cm$ pointing along $+ y$ direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the $x$ direction will be

A beam of electrons passes undeflected through mutually perpendicular electric and magnetic fields. It the electric field is switched off, and the same magnetic field is maintained, the electrons move