$A$ proton,an electron,and a Helium nucleus have the same kinetic energy. They are moving in circular orbits in a plane due to a magnetic field perpendicular to the plane. Let $r_p, r_e$,and $r_{He}$ be their respective radii. Then:

$A$ beam of electrons passes undeflected through mutually perpendicular electric and magnetic fields. If the electric field is switched off,and the same magnetic field is maintained,the electrons move

Two long parallel conductors $S_{1}$ and $S_{2}$ are separated by a distance $10 \, cm$ and carry currents of $4 \, A$ and $2 \, A$ respectively. The conductors are placed along the $x$-axis in the $X-Y$ plane. There is a point $P$ located between the conductors (as shown in the figure). $A$ charged particle of $3 \pi \, C$ is passing through the point $P$ with velocity $\overrightarrow{v} = (2 \hat{i} + 3 \hat{j}) \, m/s$; where $\hat{i}$ and $\hat{j}$ represent unit vectors along the $x$ and $y$ axes respectively. The force acting on the charged particle is $4 \pi \times 10^{-5} (-x \hat{i} + 2 \hat{j}) \, N$. The value of $x$ is:

$A$ charged particle is moving along a magnetic field line. What is the magnetic force acting on the particle? $(\sin 0^{\circ}=0, \sin \frac{\pi}{2}=1)$

$A$ charge having $q/m$ equal to $10^8 \, C/kg$ and with velocity $3 \times 10^5 \, m/s$ enters into a uniform magnetic field $0.3 \, T$ at an angle $30^{\circ}$ with the direction of the field. The radius of curvature will be ...... $cm$.

$A$ proton of velocity $(3\hat i + 2\hat j) \, ms^{-1}$ enters a magnetic field of $(2\hat j + 3\hat k) \, T$. The acceleration produced in the proton is (charge to mass ratio of proton $= 0.96 \times 10^8 \, C/kg$)