An electron is moving in a circular path under the influence of a transverse magnetic field of $3.57 \times 10^{-2}\, T $. If the value of $e/m$ is $1.76 \times 10^{11}\, C/kg $, the frequency of revolution of the electron is
$62.8 \,MHz$
$6.28 \,MHz$
$1 \,GHz$
$100 \,MHz$
A charge $q$ is moving in a magnetic field then the magnetic force does not depend upon
A uniform magnetic field $\vec B\,\, = \,\,{B_0}\,\hat j$ exists in a space. A particle of mass $m$ and charge $q$ is projected towards negative $x$-axis with speed $v$ from the a point $(d, 0, 0)$. The maximum value $v$ for which the particle does not hit $y-z$ plane is
An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement$(s)$ is/are true?
$(A)$ They will never come out of the magnetic field region.
$(B)$ They will come out travelling along parallel paths.
$(C)$ They will come out at the same time.
$(D)$ They will come out at different times.
In an experiment, electrons are accelerated, from rest, by applying, a voltage of $500 \,V.$ Calculate the radius of the path if a magnetic field $100\,mT$ is then applied. [Charge of the electron $= 1.6 \times 10^{-19}\,C$ Mass of the electron $= 9.1 \times 10^{-31}\,kg$ ]
A stream of charged particles enter into a region with crossed electric and magnetic fields as shown in the figure below. On the other side is a screen with a hole that is right on the original path of the particles. Then,