How does Ampere's law relate to magnetic field lines?

Question

I think I understand Ampere's law in the way it was taught to me by my instructor. But as the idea was given that how Gauss's Law in Electrostatics relates to electric field lines produced by charges inside the gaussian surface under consideration. We weren't given any idea that how magnetic field lines even relate to Ampere's law.
I have already searched for it on the internet including the posts present here but found nothing. All I ask for is idea that how Ampere's law relates to Magnetic field lines?.
Thank you

Answer 1

You have already an intuitive grasp of Gauss's law of electrostatics: $$\epsilon_0\oint\vec{E}\cdot d\vec{A}=Q_\text{enclosed}$$ This law links the integral of the electric field $\vec{E}$ across a closed surface to the charge $Q$ enclosed by this surface. The intuitive content of this mathematical law is:

• The electric field lines begin at positive charges and end at negative charges.
• The electric field becomes weaker at larger distance from the charges.

_{(image from Boston University - Andrew Duffy - Electric field)}

Now let us move on to Ampere's law of magnetostatics: $$\oint\vec{B}\cdot d\vec{\ell}=\mu_0 I_\text{enclosed}$$ This law links the integral of the magnetic field $\vec{B}$ along a closed line to the current $I$ enclosed by this line. The intuitive content of this mathematical law is:

• The magnetic field lines curl around currents.
• The magnetic field becomes weaker at larger distance from the currents.

_{(image from Ximera - Ampere's Law)}