Two identical wires $A$ and $B$, each of length '$I$', carry the same current $I$. Wire $A$ is bent into a circle of radius $R$ and wire $B$ is bent to form a square of side '$a$'. If $B_A$ and $B_B$ are the values of magnetic field at the centres of the circle and square respectively, then the ratio $\frac{{{B_A}}}{{{B_B}}}$ is

  • [JEE MAIN 2016]
  • A
    $\frac{{{\pi ^2}}}{{16}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$
  • B
    $\;\frac{{{\pi ^2}}}{{8\sqrt 2 }}$
  • C
    $\;\frac{{{\pi ^2}}}{8}$
  • D
    $\;\frac{{{\pi ^2}}}{{16\sqrt 2 }}$

Similar Questions

A Rowland ring of mean radius $15\; cm\;3500$ turns of wire wound on a ferromagnetic core of relative permeability $800.$ What is the magnetic field $B$ (in $T$) in the core for a magnetizing current of $1.2\; A?$

A coil of $50\, turns$ and $4\,cm$ radius carries $2\,A$ current then magnetic field at its centre is......$mT$

A cell is connected between two points of a uniformly thick circular conductor. The magnetic field at the centre of the loop will be

The magnetic induction at a point $P$ which is distant $4\, cm$ from a long current carrying wire is ${10^{ - 8}}\,Tesla$. The field of induction at a distance $12\, cm $ from the same current would be

  • [AIPMT 1990]

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field $B_1,$ at its centre when a current $I$ passes through it.The second wire is bent into a coil with  three identical loops adjacent to each other and produces magnetic field $B_2$ at the centre of the loops when current $I/3$ passes through it. The ratio $B_1 : B_2$ is

  • [JEE MAIN 2014]