$A$ $10 \; eV$ electron is circulating in a plane at right angles to a uniform magnetic field of magnetic induction $10^{-4} \; Wb/m^2$ $(1.0 \; \text{gauss})$. The orbital radius of the electron is ........ $cm$.

The radius of the path of an electron moving at a speed of $3.2 \times 10^7 \ m/s$ in a magnetic field of $6 \times 10^{-4} \ T$ perpendicular to it is (mass of electron is $9 \times 10^{-31} \ kg$ and charge of electron is $1.6 \times 10^{-19} \ C$). (in $cm$)

An electron beam is moving between two parallel plates having an electric field of $1.125 \times 10^{-6} \, N/C$. $A$ magnetic field of $3 \times 10^{-10} \, T$ is also applied so that the beam of electrons does not deflect. The velocity of the electron is ............ $m/s$.

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

An alpha particle moving with a certain speed towards the east enters a uniform magnetic field directed vertically up. The alpha particle will then move in:

An electron is moving along $+x$ direction with a velocity of $6 \times 10^{6} \, m/s$. 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: