A current loop $ABCD$ is held fixed on the plane of the paper as shown in the figure. The arcs $ BC$ (radius $= b$) and $DA $ (radius $= a$) of the loop are joined by two straight wires $AB $ and $CD$. A steady current $I$ is flowing in the loop. Angle made by $AB$ and $CD$ at the origin $O$ is $30^o $. Another straight thin wire with steady current $I_1$ flowing out of the plane of the paper is kept at the origin.
The magnitude of the magnetic field $(B)$ due to the loop $ABCD$ at the origin $(O)$ is :
$0$
$\frac{{{\mu _0}I(b - a)}}{{24ab}}$
$\frac{{{\mu _0}I}}{{4\pi }}\left[ {\frac{{b - a}}{{ab}}} \right]$
$\frac{{{\mu _0}I}}{{4\pi }}\left[ {2(b - a) + \frac{{\pi (a + b)}}{3}} \right]$
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
Two circular coils $X$ and $Y$, having equal number of turns, carry equal currents in the same sence and subtend same solid angle at point $O$. If the smaller coil $X$ is midway between $O$ and $Y$, and If we represent the magnetic induction due to bigger coil $Y$ at $O$ as $B_Y$ and that due to smaller coil $X$ at $O$ as $B_X$, then $\frac{{{B_Y}}}{{{B_X}}}$ is
Magnetic effect of current was discovered by
A circular loop of radius $r$ is carrying current I A. The ratio of magnetic field at the centre of circular loop and at a distance $r$ from the center of the loop on its axis is:
A wire carrying current $I$ has the shape as shown in adjoining figure.Linear parts of the wire are very long and parallel to $X-$axis while semicircular portion of radius $R$ is lying in $Y-Z$ plane. Magnetic field at point $O$ is