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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:

Similar Questions

Assertion: The magnetic field produced by a current-carrying solenoid is independent of its length and cross-sectional area.
Reason: The magnetic field inside the solenoid is uniform.

Two toroids with number of turns $400$ and $200$ have average radii $30 \ cm$ and $60 \ cm$ respectively. If they carry the same current,the ratio of magnetic fields in these two toroids is:

$A$ long solenoid carrying a current produces a magnetic field $B$ along its axis. If the number of turns per $cm$ is doubled and the current is made $\left(\frac{1}{3}\right)^{rd}$ of its original value,then the new value of the magnetic field will be:

$A$ toroid of $n$ turns,mean radius $R$ and cross-sectional radius $a$ carries current $I$. It is placed on a horizontal table taken as $xy$-plane. Its magnetic moment $m$ is:

$A$ toroid has a number of turns per unit length $n$ and current $i$. What is the magnetic field inside the toroid?

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