A single current carrying loop of wire carrying current $I$ flowing in anticlockwise direction seen from the $+z$ direction and lying in the $xy$ plane is shown in figure. The plot of the $\hat{j}$ component of magnetic field ($B_y$) at a distance $a$ (less than radius of the coil) and on the $yz$ plane versus $z$ coordinate looks like
Answer: (C) see figure
On the $z$-axis the field of the loop is purely along $z$. At the point $(0,a,z)$, just off the axis, the field has a small radial component, and here the radial direction is $\hat j$.
- At $z=0$ (the plane of the loop) the field is along $z$ by symmetry, so $B_y=0$.
- The field lines spread outward on one side of the loop and converge on the other, so the radial component changes sign as $z$ changes sign: $B_y$ is an odd function of $z$.
- Far from the loop $B_y\to0$.
An odd curve that is zero at the origin, has opposite-sign extrema on either side and dies away at large $|z|$ is graph (3).
Solution by Sreeraj P, M.Sc Physics