What is an Amperian loop?

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(N/A) An Amperian loop is an imaginary closed loop or path in space,chosen to apply Ampere's circuital law to calculate the magnetic field produced by a current distribution.
It is analogous to a Gaussian surface in electrostatics.
The loop is typically chosen such that the magnetic field $B$ is either constant along the path or perpendicular to it,simplifying the line integral $\oint B \cdot dl = \mu_0 I_{\text{enclosed}}$.

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State Ampere's circuital law and explain its mathematical expression.

$A$ long wire carrying a current of $18 \,A$ is kept along the axis of a long solenoid of radius $1 \,cm$. The magnetic field due to the solenoid is $8.0 \times 10^{-3} \,T$. The magnitude of the resultant magnetic field at a point $0.6 \,mm$ from the solenoid axis is (Assume $\mu_0 = 4 \pi \times 10^{-7} \,Tm/A$):

$A$ long solenoid carrying a current produces a magnetic field $B$ along its axis. If the current is doubled and the number of turns per cm is halved,the new value of the magnetic field is

$A$ toroid has a core (non-ferromagnetic) of inner radius $25 \; cm$ and outer radius $26 \; cm,$ around which $3500$ turns of a wire are wound. If the current in the wire is $11 \; A$,what is the magnetic field:
$(a)$ outside the toroid,
$(b)$ inside the core of the toroid,and
$(c)$ in the empty space surrounded by the toroid?

The magnetic flux near the axis and inside the air core solenoid of length $60 \, cm$ carrying current '$I$' is $1.57 \times 10^{-6} \, Wb$. Its magnetic moment will be $[\mu_0 = 4 \pi \times 10^{-7} \, SI \, unit$ and cross-sectional area is very small as compared to the length of the solenoid.] (in $Am^2$)

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