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(B) The direction of the magnetic field at every point on the axis of a current-carrying coil remains the same,although the magnitude varies. Hence,th

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(B) The direction of the magnetic field at every point on the axis of a current-carrying coil remains the same,although the magnitude varies. Hence,the magnetic induction for the whole $x$-axis will remain positive. Therefore,graphs $(c)$ and $(d)$ are incorrect.The magnitude of the magnetic field varies with $x$ according to the law: $B = \frac{\mu_0 NI R^2}{2(R^2 + x^2)^{3/2}}$.At $x = 0$,$B = \frac{\mu_0 NI}{2R}$,and as $x 	o \infty$,$B 	o 0$.The slope of the graph is given by $\frac{dB}{dx} = - \frac{3\mu_0 NI R^2 x}{2(R^2 + x^2)^{5/2}}$.At $x = 0$,the slope is equal to zero,which means the tangent to the graph at $x = 0$ must be parallel to the $x$-axis. Thus,the graph must have a peak at the origin with a zero slope. Comparing this with the given options,graph $(b)$ correctly represents this variation.

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