When a charged particle moving with velocity $\vec v$ is subjected to a magnetic field of induction $\vec B$, the force on it is non-zero. This implies that

Two parallel wires in the plane of the paper are distance $X _0$ apart. A point charge is moving with speed $u$ between the wires in the same plane at a distance $X_1$ from one of the wires. When the wires carry current of magnitude $I$ in the same direction, the radius of curvature of the path of the point charge is $R_1$. In contrast, if the currents $I$ in the two wires have direction opposite to each other, the radius of curvature of the path is $R_2$.

If $\frac{x_0}{x_1}=3$, the value of $\frac{R_1}{R_2}$ is.

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

A particle of mass $M$ and charge $Q$ moving with velocity $\mathop v\limits^ \to $ describes a circular path of radius $R$ when subjected to a uniform transverse magnetic field of induction $B$. The work done by the field when the particle completes one full circle is

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