
(A) The graph between magnetic susceptibility and magnetising field is as shown in (III).
(B) For \( x < a \), the magnetic field due to a current-carrying wire is given by: \[ B = \frac{\mu_0 I x}{2 \pi a^2}, \] matching graph (IV).
(C) For \( x > a \), the magnetic field due to a current-carrying wire is given by: \[ B = \frac{\mu_0 I}{2 \pi x}, \] matching graph (I).
(D) The magnetic field inside a solenoid varies with distance as shown in (II).

An infinite wire has a circular bend of radius \( a \), and carrying a current \( I \) as shown in the figure. The magnitude of the magnetic field at the origin \( O \) of the arc is given by:
Let one focus of the hyperbola \( H : \dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1 \) be at \( (\sqrt{10}, 0) \) and the corresponding directrix be \( x = \dfrac{9}{\sqrt{10}} \). If \( e \) and \( l \) respectively are the eccentricity and the length of the latus rectum of \( H \), then \( 9 \left(e^2 + l \right) \) is equal to:
