The figure shows a region of length $'l'$ with a uniform magnetic field of $0.3\, T$ in it and a proton entering the region with velocity $4 \times 10^{5}\, ms ^{-1}$ making an angle $60^{\circ}$ with the field. If the proton completes $10$ revolution by the time it cross the region shown, $l$ is close to....... $m$
(mass of proton $=1.67 \times 10^{-27} \,kg ,$ charge of the proton $\left.=1.6 \times 10^{-19}\, C \right)$
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A thin circular disk of radius $R$ is uniformly charged with density $\sigma>0$ per unit area. The disk rotates about its axis with a uniform angular speed $\omega$. The magnetic moment of die disk is
Two very long, straight and parallel wires carry steady currents $I$ and $I$ respectively. The distance between 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 this plane. The magnitude of the force due to the magnetic field acting on the charge at this instant is
A triangular shaped wire carrying $10 A$ current is placed in a uniform magnetic field of $0.5\,T$, as shown in figure. The magnetic force on segment $CD$ is $....N$ $($ Given $BC = CD = BD =5\,cm )$.
A current $i$ ampere flows in a circular arc of wire whose radius is $R$, which subtend an angle $3\pi /2$ radian at its centre. The magnetic induction at the centre is
Particles having positive charges occasionally come with high velocity from the sky towards the earth. On account of the magnetic field of earth, they would be deflected towards the
Two particles each of mass $m$ and charge $q$ are attached to the two ends of a light rigid rod of length $2R$. The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is
A horizontal rod of mass $10\, gm$ and length $10\, cm$ is placed on a smooth plane inclined at an angle of $60^\circ $ with the horizontal, with the length of the rod parallel to the edge of the inclined plane. A uniform magnetic field of induction $B$ is applied vertically downwards. If the current through the rod is $1.73$ $ampere$, then the value of $B$ for which the rod remains stationary on the inclined plane is......$Tesla$
A long insulated copper wire is closely wound as a spiral of ' $N$ ' turns. The spiral has inner radius ' $a$ ' and outer radius ' $b$ '. The spiral lies in the $X-Y$ plane and a steady current ' $I$ ' flows through the wire. The $Z$-component of the magnetic field at the center of the spiral is