1. Interpret each graph relation from physics laws

We identify the shape of each required graph.

2. Case A: Magnetic susceptibility vs magnetising field

For a magnetic material in the ordinary linear regime, $M=\chi H$ where $\chi$ is magnetic susceptibility.

For a given material (ignoring saturation/nonlinear effects), $\chi$ is approximately independent of magnetising field $H$.

So the graph of susceptibility vs magnetising field is a horizontal straight line.

Hence A corresponds to graph III.

3. Case B: Magnetic field vs distance from centre of a current carrying wire for $x<a$

Inside a long solid wire carrying uniformly distributed current, $B=\frac{\mu_0 I x}{2\pi a^2}, \qquad (x<a)$

Thus, $B\propto x$

So inside the wire, magnetic field increases linearly from the centre. This is a straight line through origin.

Hence B corresponds to graph I.

4. Case C: Magnetic field vs distance from centre of a current carrying wire for $x>a$

Outside the wire, $B=\frac{\mu_0 I}{2\pi x}, \qquad (x>a)$

Thus, $B\propto \frac{1}{x}$

So the graph is a decreasing rectangular hyperbola.

Hence C corresponds to graph IV.

5. Case D: Magnetic field inside solenoid vs distance from centre

Inside a long solenoid, magnetic field is nearly uniform near the middle and decreases near the ends. Thus along the axis, the graph is maximum and almost constant near the centre, then falls symmetrically toward the ends.

This corresponds to the usual flat-topped symmetric curve.

Hence D corresponds to graph II.

6. Final matching

So we get:

• $A \to III$
• $B \to I$
• $C \to IV$
• $D \to II$

This matches Option B.

7. Comparison with stored answer

Stored correct answer = B.

Our derived answer = B.

So they agree.