A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve z direction and lying in x y plane is shown in figure. The plot of ĵ component of magnetic field (By) at a distance 'a' (less than radius of the coil) and on y z plane vs z coordinate looks like

Solution

Physics sir · 4 steps

Picture the field lines of the loop: they spread out above it and squeeze in below it, so B_y flips sign.

1. Field direction. The current is anticlockwise when seen from +z, so by the right-hand rule the field inside the loop points along +z. The loop behaves like a small bar magnet with its north pole facing +z.
2. At z = 0. In the plane of the loop, the field is the same above and below that plane by symmetry. So it has no sideways part there, only B_z. That gives B_y = 0 at z = 0.
3. Either side. For z > 0 the field lines leave the loop and spread away from the axis, so at y = a they tilt towards +y and B_y > 0. For z < 0 the lines come in and converge towards the axis, so they tilt towards -y and B_y < 0. Far from the loop on either side, the whole field dies out, so B_y → 0.
4. So. B_y is zero at the origin, negative for z < 0 and positive for z > 0, with one extreme on each side before fading to zero. It is an odd function of z, which is graph (d).

The idea to keep. Off the axis of a loop, the sideways field is zero in the loop's plane and has opposite signs on the two faces. Lines diverge where they leave the loop and converge where they enter it.

Answer from the NTA final answer key. Solution by PrepWiser.