Mixed $H{e^ + }$ and ${O^{2 + }}$ ions (mass of $H{e^ + } = 4\,\,amu$ and that of ${O^{2 + }} = 16\,\,amu)$ beam passes a region of constant perpendicular magnetic field. If kinetic energy of all the ions is same then

Show that a force that does no work must be a velocity dependent force.

Two toroids $1$ and $2$ have total number of tums $200$ and $100 $ respectively with average radii $40\; \mathrm{cm}$ and $20 \;\mathrm{cm}$ respectively. If they carry same current $i,$ the ratio of the magnetic flelds along the two loops is

A beam of electrons is moving with constant velocity in a region having electric and magnetic fields of strength $20\;V{m^{ - 1}}$ and $0.5 T$ at right angles to the direction of motion of the electrons. What is the velocity of the electrons............ $m{s^{ - 1}}$

An electron (mass $= 9 \times 10^{-31}\,kg$. Charge $= 1.6 \times 10^{-19}\,C$) whose kinetic energy is $7.2 \times 10^{-18}$ $joule$ is moving in a circular orbit in a magnetic field of $9 \times 10^{-5} \,weber/m^2$. The radius of the orbit is.....$cm$

Two very long, straight, parallel wires carry steady currents $I$ and $-I$ respectively. The distance  etween the wires is $d$. At a certain instant of time, a point charge $q$ is at a point equidistant from the two wires, in the plane of the wires. Its instantaneous velocity $v$ is perpendicular to the plane of wires. The magnitude of the force due to the magnetic field acting on the charge at this instant is