A proton and an $\alpha - $particle enter a uniform magnetic field perpendicularly with the same speed. If proton takes $25$ $\mu \, sec$ to make $5$ revolutions, then the periodic time for the $\alpha - $ particle would be........$\mu \, sec$

What is the radius of the path of an electron (mass $9 \times 10^{-31}\;kg$ and charge $1.6 \times 10^{-19} \;C )$ moving at a speed of $3 \times 10^{7} \;m / s$ in a magnetic field of $6 \times 10^{-4}\;T$ perpendicular to it? What is its frequency? Calculate its energy in $keV$. ( $\left.1 eV =1.6 \times 10^{-19} \;J \right)$

A particle of mass $m$ and charge $q$ enters a region of magnetic field (as shown) with speed $v$. There is a region in which the magnetic field is absent, as shown. The particle after entering the region collides elas tically with a rigid wall. Time after which the velocity of particle becomes anti parallel to its initial velocity is

In toroid magnetic field on axis will be the radius $=0.5\, cm ,$ current $=1.5\, A ,$ turns $=250,$ permeability $=700$ (in Tesla)

An electron is moving in the north direction. It experiences a force in vertically upward direction. The magnetic field at the position of the electron is in the direction of

Two identical charged particles enter a uniform magnetic field with same speed but at angles $30^o$ and $60^o$ with field. Let $a, b$ and $c$ be the ratio of their time periods, radii and pitches of the helical paths than