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 $BC = CD = BD =5\,cm )$.

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 ?

$A, B$ and $C$ are parallel conductors of equal length carrying currents $I, I$ and $2I$ respectively. Distance between $A$ and $B$ is $x$. Distance between $B$ and $C$ is also $x$. ${F_1}$ is the force exerted by $B$ on $A$ and $F_2$ is the force exerted by $B$ on $A$ choose the correct answer

A long straight wire carrying current of $25$ $\mathrm{A}$ rests on a table as shown in figure. Another wire $\mathrm{PQ}$ of length $1$ $\mathrm{m}$, mass $2.5$ $\mathrm{g}$ carries the same current but in the opposite direction. The wire $\mathrm{PQ}$ is free to slide up and down. To what height will $\mathrm{PQ}$ rise ? 

The wires which connect the battery of an automobile to its starting motor carry a current of $300\; A$ (for a short time). What is the force per unit length between the wires if they are $70\; cm$ long and $1.5\; cm$ apart? Is the force attractive or repulsive?

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........$N-m$