A)
B)
C)
D)
Correct Answer: B
Solution :
Direction of magnetic field at every point on axis of a current carrying coil remains same though magnitude varies. Hence magnetic induction for whole the x-axis will remain positive. Therefore, (c) and (d) are wrong. Magnitude of magnetic field will very with x according to law, \[B=\frac{{{\mu }_{0}}NI{{R}^{2}}}{2{{({{R}^{2}}+{{x}^{2}})}^{3/2}}}\]. Hence, at \[x=0,\ B=\frac{{{\mu }_{0}}NI}{2R}\] and when \[x\to \infty ,\ B\to 0.\] Slope of the graph will be \[\frac{dB}{dx}=-\frac{3{{\mu }_{0}}NI{{R}^{2}}.x}{2{{({{R}^{2}}+{{x}^{2}})}^{5/2}}}\]. It means, at x = 0, slope is equal to zero or tangent to the graph at x = 0, must be parallel to x-axis. Hence (b) is correct and (a) is wrong.
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