A square-shaped conducting wire loop of dimension moving parallel to the $X$-axis approaches a square region of size $b(a < b)$, where a uniform magnetic field $B$ exists pointing into the plane of the paper (see figure). As the loop passes through this region, the plot correctly depicting its speed $v$ as a function of $x$ is

A rectangular coil $20\,cm \times 20\,cm$ has $100$ $turns$ and carries a current of $1\, A$. It is placed in a uniform magnetic field $B =0.5\, T$ with the direction of magnetic field parallel to the plane of the coil. The magnitude of the torque required to hold this coil in this position is........$N-m$

Consider the inferences given below in respect of the following current loop of wire kept is a magnetic field $\vec B$

$A.$ The force on the element $AC$ of the wire is $\frac{{\sqrt 3 }}{2}\,ILB$ directed into the page

$B.$ The force on the element $AB$ of the wire is $\frac{{\sqrt 3 }}{2}\,ILB$ directed into the page

$C.$ The total force on the loop $ABCA$ is zero.

Which of the above is /are not true ?

Two parallel, long wires are kept $0.20\,m$ apart in vacuum, each carrying current of $x$ in the same direction. If the force of attraction per meter of each wire is $2 \times 10^{-6}\,N$, then the value of $x$ is approximately

A rectangular loop of wire shown below is coplanar with a long wire carrying current $I$. The loop is pulled to the right a s indicated. What are the directions of the induced current in the loop and the magnetic forces on the left and the right sides of the loop?

A vertical wire carrying a current in the upward direction is placed in horizontal magnetic field directed towards north. The wire will experience a force directed towards