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(D) According to Ampere's Circuital Law,the line integral of the magnetic field $\vec{B}$ around any closed loop is equal to $\mu_0$ times the total c

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Zero

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(D) According to Ampere's Circuital Law,the line integral of the magnetic field $\vec{B}$ around any closed loop is equal to $\mu_0$ times the total current $I_{enclosed}$ passing through the surface bounded by the loop.For a hollow cylinder of infinite length with a surface current density $\lambda$ (current per unit length along the axis),the magnetic field inside the cylinder is zero. This is because the current flows along the circumference,creating a solenoid-like configuration where the magnetic field is confined to the interior of the solenoid (if it were a coil) or,in this specific case of a surface current flowing around the cylinder,the field inside is zero due to the symmetry and the nature of the current distribution.Alternatively,using Ampere's law for a loop inside the cylinder,the enclosed current is zero,hence $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enclosed} = 0$,which implies $B = 0$ inside the hollow cylinder.

$A$ hollow cylinder of infinite length carries a uniform current per unit length $\lambda$ along its circumference,as shown. The magnetic field inside the cylinder is:

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