What are electromagnets?

In the following diagram,there is a straight wire carrying a current $I$. Consider a circular path with radius $R$ near it. If $\vec{B}_T$ is the tangential component of the magnetic field along the circular path,then find the value of the integral $\oint \vec{B}_T \cdot d\vec{l}$.

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 $Am^2$)

$A$ solenoid is $1 \ m$ long and $4 \ cm$ in diameter. It has five layers of windings of $1000$ turns each and carries a current of $7 \ A$. The magnetic field at the centre of the solenoid is

In a co-axial straight cable,the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero:

Write the equation for the magnetic field at an inside point of a very long solenoid.