$A$ charged particle with a velocity $2 \times 10^{3} \ ms^{-1}$ passes undeflected through electric and magnetic fields in mutually perpendicular directions. The magnetic field is $1.5 \ T$. The magnitude of the electric field will be:

An electron is allowed to move with constant velocity along the axis of a current-carrying straight solenoid. Which of the following statements are correct?
$A.$ The electron will experience magnetic force along the axis of the solenoid.
$B.$ The electron will not experience magnetic force.
$C.$ The electron will continue to move along the axis of the solenoid.
$D.$ The electron will be accelerated along the axis of the solenoid.
$E.$ The electron will follow a parabolic path inside the solenoid.
Choose the correct answer from the options given below:

$A$ proton and a helium nucleus are shot into a magnetic field at right angles to the field with the same kinetic energy. The ratio of their radii is:

$A$ proton of velocity $v = (3 \hat{i} + 2 \hat{j}) \ m/s$ enters a magnetic field of induction $B = (2 \hat{j} + 3 \hat{k}) \ T$. The acceleration produced in the proton in $m/s^2$ is (Specific charge of proton $= 0.96 \times 10^8 \ C/kg$)

An electron of mass $m$ and charge $q$ is travelling with a speed $v$ along a circular path of radius $r$ at right angles to a uniform magnetic field $B$. If the speed of the electron is doubled and the magnetic field is halved,then the resulting path would have a radius of:

An electron with energy $0.1 \, keV$ moves at a right angle to the Earth's magnetic field of $1 \times 10^{-4} \, Wb/m^2$. The frequency of revolution of the electron will be. (Take mass of electron $= 9.0 \times 10^{-31} \, kg$)