Three infinite wires are arranged in space in three dimensions.(along $x, y$ and $z$ axis) as shown. Each wire carries current $i$ . Find magnetic field at $A$
$ - \frac{{{\mu _0}i}}{{2\pi r}}\hat i - \frac{{{\mu _0}i}}{{2\pi r}}\hat j - \frac{{{\mu _0}i}}{{\pi r}}\hat k$
$ - \frac{{{\mu _0}i}}{{4\pi r}}\hat i + \frac{{{\mu _0}i}}{{4\pi r}}\hat j - \frac{{{\mu _0}i}}{{\pi r}}\hat k$
$ \frac{{{\mu _0}i}}{{4\pi r}}\hat i + \frac{{{\mu _0}i}}{{4\pi r}}\hat j - \frac{{{\mu _0}i}}{{\pi r}}\hat k$
$ \frac{{{\mu _0}i}}{{2\pi r}}\hat i + \frac{{{\mu _0}i}}{{2\pi r}}\hat j - \frac{{{\mu _0}i}}{{\pi r}}\hat k$
A square frame of side I carries a current $i$. The magnetic field at its centre is $B$. The same current is passed through a circular coil having the same perimeter as the square. The field at the centre of the circular coil is $B^{\prime}$. The ratio of $\frac{B}{B^{\prime}}$ is
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
An electron moving in a circular orbit of radius $r$ makes $n$ rotations per second. The magnetic field produced at the centre has magnitude
In the diagram, $I_1$ , $I_2$ are the strength of the currents in the loop and infinite long straight conductor respectively. $OA = AB = R$ . The net magnetic field at the centre $O$ is zero. Then the ratio of the currents in the loop and the straight conductor is
Show magnetic field lines due to current carrying loop.