$A$ proton enters a magnetic field of flux density $1.5 \,Wb \,m^{-2}$ with a velocity of $2 \times 10^7 \,ms^{-1}$ at an angle of $30^{\circ}$ with the field. The force on the proton will be

$A$ particle of mass $m = 1.67 \times 10^{-27} \, kg$ and charge $q = 1.6 \times 10^{-19} \, C$ enters a region of uniform magnetic field of strength $B = 1 \, T$ along the direction shown in the figure. The angle of incidence is $45^{\circ}$ and the angle of emergence is also $45^{\circ}$. The time spent by the particle in the magnetic field is $...... \, ns$.

$A$ mixed beam of $He^+$ and $O^{2+}$ ions (mass of $He^+ = 4 \ amu$ and that of $O^{2+} = 16 \ amu$) passes through a region of a constant perpendicular magnetic field. If the kinetic energy of all the ions is the same,then:

$A$ particle of charge $q$ moves with a velocity $\vec{V} = a \hat{i}$ in a magnetic field $\vec{B} = b \hat{j} + c \hat{k}$,where $a$,$b$,and $c$ are constants. The magnitude of the force experienced by the particle is:

$A$ proton is moving with a uniform velocity of $10^{6} \ m/s$ along the $Y$-axis, under the joint action of a magnetic field along the $Z$-axis and an electric field of magnitude $2 \times 10^{4} \ V/m$ along the negative $X$-axis. If the electric field is switched off, the proton starts moving in a circle. The radius of the circle is nearly: (Given: $\frac{e}{m}$ ratio for proton $= 10^{8} \ C/kg$) (in $m$)

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 $cm$)