$A$ particle of specific charge $(q/m)$ is projected from the origin of coordinates with initial velocity $(u\hat{i} - v\hat{j})$. Uniform electric and magnetic fields exist in the region along the $+y$ direction,of magnitude $E$ and $B$ respectively. The particle will definitely return to the origin once if:

Two long current-carrying thin wires,both with current $I$,are held by insulating threads of length $L$ and are in equilibrium as shown in the figure,with threads making an angle $\theta$ with the vertical. If the wires have mass $\lambda$ per unit length,then the value of current $I$ is ($g =$ gravitational acceleration).

An electron is projected with velocity $v_0$ in a uniform electric field $E$ perpendicular to the field. Again,it is projected with velocity $v_0$ perpendicular to a uniform magnetic field $B$. If $r_1$ is the initial radius of curvature just after entering the electric field and $r_2$ is the initial radius of curvature just after entering the magnetic field,then the ratio $r_1:r_2$ is equal to:

If an observer is moving with respect to a stationary electron,then he observes:

Two charged particles $A$ and $B$,each of charge $+e$ and masses $12 \, amu$ and $13 \, amu$ respectively,follow a circular trajectory in chamber $X$ after passing through a velocity selector as shown in the figure. Both particles enter the velocity selector with a speed of $1.5 \times 10^6 \, ms^{-1}$. $A$ uniform magnetic field of strength $1.0 \, T$ is maintained within the chamber $X$ and in the velocity selector,directed into the plane ($-z$ direction).

Assertion : $A$ charge,whether stationary or in motion,produces a magnetic field around it.
Reason : Moving charges produce only electric field in the surrounding space.