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

Two charged particles traverse identical helical paths in a completely opposite sense in a uniform magnetic field $B = B_0 \hat k$ .

In a chamber, a uniform magnetic field of $6.5 \;G \left(1 \;G =10^{-4} \;T \right)$ is maintained. An electron is shot into the field with a speed of $4.8 \times 10^{6} \;m s ^{-1}$ normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit.

$\left(e=1.5 \times 10^{-19} \;C , m_{e}=9.1 \times 10^{-31}\; kg \right)$

In a certain region static electric and magnetic fields exist. The magnetic field is given by $\vec B = {B_0}\left( {\hat i + 2\hat j - 4\hat k} \right)$. If a test charge moving with a velocity $\vec v = {v_0}\left( {3\hat i - \hat j + 2\hat k} \right)$ experiences no force in that region, then the electric field in the region, in $SI\, units$, is

Two charges of same magnitude move in two circles of radii $R_1=R$ and $R_2=2 R$ in a region of constant uniform magnetic field $B _0$. The work $W_1$ and $W_2$ done by the magnetic field in the two cases respectively, are such that

A charge $+ Q$ is moving upwards vertically. It enters a magnetic field directed to the north. The force on the charge will be towards