What is a solenoid? And what is a long solenoid? Explain.

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(N/A) solenoid is a long wire wound in a close-packed helix. When an electric current flows through it,it produces a magnetic field similar to that of a bar magnet.
$A$ long solenoid is defined as a solenoid whose length $(L)$ is much greater than its radius $(R)$,i.e.,$L \gg R$.
In a long solenoid,the magnetic field inside is nearly uniform and directed along the axis of the solenoid. The magnetic field outside the solenoid is negligible. For an ideal long solenoid,the magnetic field at any point inside is given by $B = \mu_0 n I$,where $\mu_0$ is the permeability of free space,$n$ is the number of turns per unit length,and $I$ is the current flowing through the solenoid.

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$A$ long cylindrical conductor with a large cross-section carries an electric current distributed uniformly over its cross-section. The magnetic field due to this current is:

$A$ steady current $I$ flows along an infinitely long hollow cylindrical conductor of radius $R$. This cylinder is placed coaxially inside an infinite solenoid of radius $2R$. The solenoid has $n$ turns per unit length and carries a steady current $I$. Consider a point $P$ at a distance $r$ from the common axis. The correct statement$(s)$ is (are) :
$(A)$ In the region $0 < r < R$,the magnetic field is non-zero.
$(B)$ In the region $R < r < 2R$,the magnetic field is along the common axis.
$(C)$ In the region $R < r < 2R$,the magnetic field is tangential to the circle of radius $r$,centered on the axis.
$(D)$ In the region $r > 2R$,the magnetic field is non-zero.

$A$ $50 \ cm$ long solenoid has a winding of $400$ turns. What current must pass through it to produce a magnetic field of induction $4 \pi \times 10^{-3} \ T$ at the centre (in $A$)?

What is a solenoid? Provide information about the magnetic field through a qualitative discussion.

What is the magnetic field outside an ideal solenoid?

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