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

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 $1$ $tesla$ along the direction shown in the figure. The speed of the particle is $10^7\, m/s.$ The magnetic field is directed along the inward normal to the plane of the paper. The particle enters the field at $C$ and leaves at $D.$ Then the angle $\theta$ must be :-.........$^o$

The magnetic moments associated with two closely wound circular coils $A$ and $B$ of radius $r_A=10 cm$ and $r_B=20 cm$ respectively are equal if: (Where $N _A, I _{ A }$ and $N _B, I _{ B }$ are number of turn and current of $A$ and $B$ respectively)

The magnetic force acting on a charged particle of charge $-2\, \mu  C$ in a magnetic field of $2\, T$ acting in $y$ direction, when the particle velocity is $(2i + 3 j) \times  10^6\,\, m/s$ is

An electron (mass = $9.1 \times {10^{ - 31}}$ $kg$; charge = $1.6 \times {10^{ - 19}}$ $C$) experiences no deflection if subjected to an electric field of $3.2 \times {10^5}$ $V/m$, and a magnetic fields of $2.0 \times {10^{ - 3}} \,Wb/m^2$. Both the fields are normal to the path of electron and to each other. If the electric field is removed, then the electron will revolve in an orbit of radius.......$m$

A moving charge will gain energy due to the application of