A proton of velocity $\left( {3\hat i + 2\hat j} \right)\,ms^{-1}$ enters a magnetic field of $(2\hat j + 3\hat k)\, tesla$. The acceleration produced in the proton is (charge to mass ratio of proton $= 0.96 \times10^8\,Ckg^{-1}$)
$2.88 \times {10^8}\left( {2\hat i - 3\hat j} \right)\,m/s^2$
$2.88 \times {10^8}\left( {2\hat i - 3\hat j + 2\hat k} \right)\,m/s^2$
$2.88 \times {10^8}\left( {2\hat i + 3\hat k} \right)\,m/s^2$
$2.88 \times {10^8}\left( {\hat i - 3\hat j + 2\hat k} \right)\,m/s^2$
Mixed $H{e^ + }$ and ${O^{2 + }}$ ions (mass of $H{e^ + } = 4\,\,amu$ and that of ${O^{2 + }} = 16\,\,amu)$ beam passes a region of constant perpendicular magnetic field. If kinetic energy of all the ions is same then
A collimated beam of charged and uncharged particles is directed towards a hole marked $P$ on a screen as shown below. If the electric and magnetic fields as indicated below are turned $ON$
A magnetic field set up using Helmholtz coils is uniform in a small region and has a magnitude of $0.75 \;T$. In the same region, a uniform electrostatic field is maintained in a direction normal to the common axis of the coils. A narrow beam of (single species) charged particles all accelerated through $15\; kV$ enters this region in a direction perpendicular to both the axis of the coils and the electrostatic field. If the beam remains undeflected when the electrostatic field is $9.0 \times 10^{-5} \;V\, m ^{-1},$ make a simple guess as to what the beam contains. Why is the answer not unique?
In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential $V$ and then made to describe semicircular paths of radius $R$ using a magnetic field $B$. If $V$ and $B$ are kept constant, the ratio $\left( {\frac{{{\text{charge on the ion}}}}{{{\text{mass of the ion}}}}} \right)$ will be proportional to
An electron is projected with velocity $v_0$ in a uniform electric field $E$ perpendicular to the field. Again it is projetced with velocity $v_0$ perpendicular to a uniform magnetic field $B/$ If $r_1$ is initial radius of curvature just after entering in the electric field and $r_2$ is initial radius of curvature just after entering in magnetic field then the ratio $r_1:r_2$ is equal to