Find the magnetic field at the point $P$ in figure. The curved portion is a semicircle connected to two long straight wires.
$\frac{\mu_0 i}{2 r}\left(1+\frac{2}{\pi}\right)$
$\frac{\mu_0 i}{2 r}\left(1+\frac{1}{\pi}\right)$
$\frac{\mu_0 i}{2 r}\left(\frac{1}{2}+\frac{1}{2 \pi}\right)$
$\frac{\mu_0 i}{2 r}\left(\frac{1}{2}+\frac{1}{\pi}\right)$
An arc of a circle of radius $R$ subtends an angle $\frac{\pi }{2}$ at the centre. It carries a current $i$. The magnetic field at the centre will be
Two concentric coils $X$ and $Y$ of radii $16 \,\,cm$ and $10 \,\,cm$ lie in the same vertical plane containing $N-S$ direction. $X$ has $20$ $turns$ and carries $16 \,\,A.$ $Y$ has $25$ $turns$ $\&$ carries $18\,A$. $X$ has current in anticlockwise direction and $Y$ has current in clockwise direction for an observer, looking at the coils facing the west. The magnitude of net magnetic field at their common centre is
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
For the magnetic field to be maximum due to a small element of current carrying conductor at a point, the angle between the element and the line joining the element to the given point must be.......$^o$
A cell is connected between the points $A$ and $C$ of a circular conductor $ABCD$ of centre $O$ with angle $AOC = {60^o}$. If ${B_1}$ and ${B_2}$ are the magnitudes of the magnetic fields at $O$ due to the currents in $ABC$ and $ADC$ respectively, the ratio $\frac{{{B_1}}}{{{B_2}}}$ is