Consider two infinitely long wires parallel to Z-axis carrying same current I in the positive z-direction. One wire passes through the point L at coordinates ($$-$$1, +1) and the other wire passes through the point M at coordinates ($$-$$1, $$-$$1). The resultant magnetic field at the origin O will be

A thin charged rod is bent into the shape of a small circle of radius R, the charge per unit length of the rod being $$\lambda$$. The circle is rotated about its axis with a time period T and it is found the magnetic field at a distance d away (d >> R) from the centre and on the axis, varies as $$R^m \over d^n$$. The values of m and n respectively are

For two types of magnetic materials A and B, variation of $$1\over\chi$$ ($$\chi$$ : susceptibility) versus temperature T is shown in the figure. Then,

As shown in the figure, a single conducting wire is bent to form a loop in the form of a circle of radius r concentrically inside a square of side a, where a : r = 8 : $$\pi $$. A battery B drives a current through the wire. If the battery B and the gap G are of negligible sizes, determine the strength of magnetic field at the common centre O.