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Question 12

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

image

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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