A circular coil is in $y-z$ plane with centre at the origin. The coil is carrying a constant current. Assuming direction of magnetic field at $x = -25\, cm$ to be positive direction of magnetic field, which of the following graphs shows variation of magnetic field along $x-$ axis
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Direction of magnetic field at every point on the axis of a current carrying circular coil remains same. Though its magnitude varies. Hence $\mathrm{B}$ always remains positive.
Therefore, $( 3)$ and $( 4)$ are wrong. Further,
$\mathrm{B}=\frac{\mu_{0} \mathrm{Nia}^{2}}{2\left(\mathrm{a}^{2}+\mathrm{x}^{2}\right)^{3 / 2}}$
where a is the radius of the coil
At $\mathrm{x}=0, \quad \mathrm{B}=\frac{\mu_{0} \mathrm{Ni}}{2 \mathrm{a}}$
when $\mathrm{x} \rightarrow \infty, \mathrm{B} \rightarrow 0$
Slope of the graph will be $\frac{\mathrm{dB}}{\mathrm{dx}}=\frac{3 \mu_{0} \mathrm{Nia}^{2} \mathrm{x}}{2\left(\mathrm{a}^{2}+\mathrm{x}^{2}\right)^{5 / 2}}$
which means at $\mathrm{x}=0,$ slope is equal to zero or tangent to the graph at $\mathrm{x}=0$ must be parallel to $x$ - axis. Hence $(2)$ is correct and $(1)$ is wrong.
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