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A single current carrying loop of wire carrying current $$I$$ flowing in anticlockwise direction seen from $$+ve$$ z direction and lying in $$xy$$ plane is shown in figure. The plot of $$\hat{j}$$ component of magnetic field $$(B_y)$$ at a distance $$a$$ (less than radius of the coil) and on $$yz$$ plane vs $$z$$ coordinate looks like
The circular loop lies in the $$yz$$ plane and its axis is along the $$x$$-axis.
Current is anticlockwise when viewed from $$+z$$-direction.
We need variation of :
$$B_y(0,a,z)$$
where point lies in the $$yz$$ plane at fixed :
$$y=a$$
with
$$a<R$$
Due to symmetry :
For every point at $$+z$$ there exists a symmetric point at $$-z$$.
Hence,
$$B_y(0,a,z)$$
is an even function of $$z$$.
At centre :
$$z=0$$
the magnetic field has maximum $$y$$-component.
As $$|z|$$ increases, the field decreases symmetrically.
Therefore :
- $$B_y$$ is maximum at $$z=0$$
- decreases symmetrically on both sides
- remains positive throughout
Hence the correct graph is the symmetric bell-shaped curve.
Final Answer :
$$\boxed{\text{Option D}}$$
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