A velocity selector is used to select alpha particles of energy $200 \mathrm{KeV}$. From a beam containing particles of several energies. The electric field strength is $900 \mathrm{kV} {\mathrm{m}}^{-1}$. What must be the magnetic field strength in $\mathrm{mT}$?

A velocity selector consists of electric field $\overrightarrow{E}=E \hat{\mathrm{k}}$ and magnetic field $\overrightarrow{B}=B \hat{\mathrm{j}}$ with $B=12 \mathrm{mT}$. The value $E$ required for an electron of energy $728\mathrm{eV}$ moving along the positive $\mathrm{x}$-axis to pass undeflected is 

(Given, mass of electron $=9.1\times {10}^{-31} \mathrm{kg}$)

In a region, an electric field $\overrightarrow{E}=5x^3 \hat{j} {\mathrm{NC}}^{-1}$ and a magnetic field of $\overrightarrow{B}=0.1 \hat{k} \mathrm{T}$ are applied. A beam of positively charged particles is projected along X-direction. Find the velocity of particles that move undeflected in these crossed fields.

At a place, an electric field and a magnetic field are in the downward direction. There an electron moves in the downward direction. Hence this electron.____________.

A proton enters a perpendicular uniform magnetic field B at origin along the positive x-axis with a velocity v as shown in the figure. Then it will follow the following path. [The magnetic field is directed into the paper].

A beam of alpha particles passes undeflected  through a velocity selector having electric and magnetic fields of $120\mathrm{kV}/\mathrm{m}$ and $60 \mathrm{mT}$,

respectively. The velocity of the beam is :

A particle a mass of ${10}^{-2} \mathrm{kg}$ carries a charge of $5\times {10}^{-8}\mathrm{C}$. The particle is given an initial horizontal velocity of ${10}^5{ \mathrm{ms}}_{}^{-1}$ in the presence of electric field $\overrightarrow{E}$ and magnetic field $\overrightarrow{\mathrm{B}}$. To keep the particle moving in a horizontal direction, it is necessary that

(i) $\overrightarrow{B}$ should be perpendicular, to the direction of velocity and $\overrightarrow{E}$ should be along the direction of velocity.

(ii) Both $\overrightarrow{B}$ and $\overrightarrow{E}$ should be along the direction of velocity.

(iii) Both $\overrightarrow{B}$ and $\overrightarrow{E}$ are mutually perpendicular and perpendicular to the direction of velocity.

(iv) $\overrightarrow{B}$ should be along the direction of velocity and $\overrightarrow{E}$ should be perpendicular to the direction of velocity.

Which one of the following pairs of statements is possible?