A long straight wire carries a current along the 'Z' axis. One can find two points in the plane perpendicular to the conductor such that

I) The magnetic fields are equal

II) The direction of the magnetic fields are perpendicular

III) Magnitudes of the magnetic fields are equal

IV) The field at one point is opposite to that at the other point.

Given Statements:

I) The magnetic fields are equal

II) The direction of the magnetic fields are perpendicular

III) Magnitudes of the magnetic fields are equal

IV) The field at one point is opposite to that at the other point.

Detailed Solution:

Consider a current Carrying wire lying along $z$axis.

II)Let two points on $xy$ plane $[A, B]$ on the same side of the wire. Then the magnitudes will be different but, direction will be same.

III)Lets tare two points$( A\&C )$ equidistant from the wire, so she magnitude will be same as $B=\frac{{\mu }_o\text{i }}{2\pi \left(d\right)}\to$that is same.

IV)Since these two points $( A\&C )$ are on opposite sides of wine, the direction of magnetic field will be opposite.

Hence, the correct option is C.