Two long parallel wires carrying equal current separated by $1\,m$, exert a force of $2 \times {10^{ - 7}}\,N/m$ on one another. The current flowing through them is
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An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of $i$ $ampere$ and the radius of the circular loop is $r$ $metre$. Then the magnetic induction at its centre will be
A beam of well collimated cathode rays travelling with a speed of $5 \times {10^6}\,m{s^{ - 1}}$ enter a region of mutually perpendicular electric and magnetic fields and emerge undeviated from this region. If $| B |=0.02\; T$, the magnitude of the electric field is
At $t$ = $0$, a positively charged particle of mass $m$ is projected from the origin with velocity $u_0$ at an angle $37^o $ from the $x-$axis as shown in the figure. A constant magnetic field ${\vec B_0} = {B_0}\hat j$ is present in space. After a time interval $t_0$ velocity of particle may be:-
Two very long, straight and insulated wires are kept at $90^o$ angle from each other In $xy -$ plane as shown in the figure. These wires carry current of equal magnitude $I$, whose directions are shown in the figure. The net magnetic field at point $P$ will be
A semi circular arc of radius $r$ and a straight wire along the diameter, both are carrying same current $i.$ Find out magnetic force per unit length on the small element $P$, which is at the centre of curvature.
Magnetic fields at two points on the axis of a circular coil at a distance of $0.05\, m$ and $0.2\, m$ from the centre are in the ratio $8: 1.$ The radius of coil is .......... $m$
A conducting wire bent in the form of a parabola $y^2 = 2x$ carries a current $i = 2 A$ as shown in figure. This wire is placed in a uniform magnetic field $\vec B = - 4\,\hat k$ $Tesla$. The magnetic force on the wire is (in newton)