Ionized hydrogen atoms and $\alpha$ -particles with same momenta enters perpendicular to a constant magnetic field $B$. The ratio of their radii of their paths $\mathrm{r}_{\mathrm{H}}: \mathrm{r}_{\alpha}$ will be
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Two identical charged particles enter a uniform magnetic field with same speed but at angles $30^o$ and $60^o$ with field. Let $a, b$ and $c$ be the ratio of their time periods, radii and pitches of the helical paths than
A current $I$ flows along the length of a thin walled, long metallic hollow cylinder of radius $R$, distributed uniformly on its surface then pressure on the wall will be
In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a
Two long current carrying thin wires, both with current $I$, are held by insulating threads oflength $L$ and are in equilibrium as shown in the figure, with threads making an angle '$\theta$' with the vertical. If wires have mass $\lambda$ per unit length then the value of $l$ is
($g =$ gravitational acceleration)
An infinitely long, straight conductor $AB$ is fixed and a current is passed through it. Another movable straight wire $CD$ of finite length and carrying current is held perpendicular to it and released. Neglect weight of the wire
$AB$ and $CD$ are smooth parallel rails, separated by a distance $l$, and inclined to the horizontal at an angle $\theta$ . $A$ uniform magnetic field of magnitude $B$, directed vertically upwards, exists in the region. $EF$ is a conductor of mass $m$, carrying a current $i$. For $EF$ to be in equilibrium,
A particle is projected with a velocity ( $10\ m/s$ ) along $y-$ axis from point $(2, 3)$ . Magnetic field of $\left( {3\hat i + 4\hat j} \right)$ Tesla exist uniformly in the space. Its speed when particle passes through $y-$ axis for the third time is : (neglect gravity)