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An electron gun is placed inside a long solenoid of radius $\mathrm{R}$ on its axis. The solenoid has $\mathrm{n}$ turns/length and carries a current $I$. The electron gun shoots an electron along the radius of the solenoid with speed $v$. If the electron does not hit the surface of the solenoid, maximum possible value of ${v}$ is (all symbols have their standard meaning)
Two coaxial solenoids of different radii carry current $I$ in the same direction. Let $\;{\overrightarrow {\;F} _1}$ be the magnetic force on the inner solenoid due to the outer one and $\;{\overrightarrow {\;F} _2}$ be the magnetic force on the outer solenoid due to the inner one. Then
A wire is bent in the form of an equilateral triangle of side $100 \,cm$ and carries a current of $2 \,A$. It is placed in a magnetic field of induction $2.0 \,T$ directed perpendicular into the plane of paper. The direction and magnitude of magnetic force acting on each side of the triangle will be
A square shaped wire loop of mass $m$, resistance $R$ and side $a$ moving speed $v_{0}$, parallel to the $X$-axis, enters a region of uniform magnetic field $B$, which is perpendicular to the plane of the loop. The speed of the loop changes with distance $x(x < a)$ in the field, as
The radius of a circular ring of wire is $R$ and it carries a current of $I\,ampere$. At its centre a smaller ring of radius $r$ with current $i$ and $N\, turns$ is placed. Assuming that the planes of two rings are perpendicular to each other and the magnetic induction produced at the centre of bigger ring is constant, then the torque acting on smaller ring will be
A circular loop of radius $0.0157\,m$ carries a current of $2.0\, amp$. The magnetic field at the centre of the loop is$({\mu _0} = 4\pi \times {10^{ - 7}}\,weber/amp - m)$
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:-
An electron accelerated through a potential difference $V$ enters a uniform transverse magnetic field and experiences a force $F$. If the accelerating potential is increased to $2V$, the electron in the same magnetic field will experience a force