A proton and an alpha particle are separately projected in a region where a uniform magnetic field exists. Their initial velocities are perpendicular to direction of magnetic field. If both the particles move around magnetic field in circles of equal radii, the ratio of momentum of proton to alpha particle $\left( {\frac{{{P_p}}}{{{P_\alpha }}}} \right)$ is
$1$
$0.5$
$2$
$0.25$
A long solenoid has $100\,turns/m$ and carries current $i.$ An electron moves with in the solenoid in a circle of radius $2·30\,cm$ perpendicular to the solenoid axis. The speed of the electron is $0·046\,c$ ($c =$ speed of light). Find the current $i$ in the solenoid (approximate).....$A$
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.
Mark the correct statement
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