The magnetic induction at the centre $O$ is:

Two long parallel wires are at a distance $2d$ apart. They carry steady equal currents flowing out of the plane of the paper,as shown. The variation of the magnetic field $B$ along the line $XX'$ is given by

Two long parallel wires separated by $0.1 \ m$ carry currents of $1 \ A$ and $2 \ A$,respectively,in opposite directions. $A$ third current-carrying wire parallel to both of them is placed in the same plane such that it feels no net magnetic force. It is placed at a distance of

The magnetic field at point $O$ for the given circuits is provided. Which of the following is correct?

$(i)$	$(ii)$	$(iii)$
$(A). \frac{\mu_0 i}{2r} \odot$	$(A). \frac{\mu_0}{2\pi} \frac{i}{r}(\pi - 2)$	$(A). \frac{\mu_0}{2r} \frac{2i}{r}(\pi + 1) \otimes$
$(B). \frac{\mu_0 i}{2r} \otimes$	$(B). \frac{\mu_0 i}{4\pi} \frac{i}{r}(\pi + 2) \otimes$	$(B). \frac{\mu_0 i}{4r} \frac{2i}{r}(\pi - 1) \otimes$
$(C). \frac{3\mu_0 i}{8r} \otimes$	$(C). \frac{\mu_0 i}{4r} \otimes$	$(C). \text{Zero}$
$(D). \frac{3\mu_0 i}{8r} \odot$	$(D). \frac{\mu_0 i}{4r} \odot$	$(D). \text{Infinite}$

When the current flowing in a circular coil is doubled and the number of turns of the coil in it is halved,the magnetic field at its centre will become

The magnitude of the force per unit length acting on a thin wire carrying a current $I=8 \text{ A}$ at a point $O$,if the wire is bent as shown in the figure with a radius $R=10 \pi \text{ cm}$,is (in $\mu \text{N/m}$)