To add to <PERSON>'s answer, I'll give you two scenarios where this equation would be useful. First, notice that this is <PERSON>'s extension of <PERSON>'s law, meaning you can apply it to situations where a magnetic field exists but there is no current (e.g inside a capacitor with an alternating current). Let's first consider the situation where you'd like to find the magnetic field produced by a current carrying wire. We will take the Amperian loop to be a concentric circle around the wire. We know that:
$$\oint\vec{B}\cdot d\vec{s}= 2\pi rB$$
since the magnetic field is always parallel to the loop (by the right hand rule), and the path length is $2\pi r$ where $r$ is the distance from the wire. 418
We also know that:
$$\mu_0I+\mu_0\epsilon_o\frac{d\Phi_e}{dt} = \mu_0I$$
since there is no displacement current in this situation. This allows us to find an equation for the magnitude of $B$:
$$B=\frac{\mu_0I}{2\pi r}$$
Now let's consider the case of finding the magnetic field inside a capacitor $(r<R)$ with two circular plates or radius $R$, and with an alternating current in the circuit. Taking the same Amperian loop as before, we also have:
$$\oint\vec{B}\cdot d\vec{s}= 2\pi rB$$
However, in this situation, we have:
$$\mu_0I+\mu_0\epsilon_o\frac{d\Phi_e}{dt} = \mu_0\epsilon_o\frac{d\Phi_e}{dt}$$
because we know that there is no current through a capacitor.
If we take $E=E_0 sin(\omega t)$ for an alternating current, we know that $\Phi_E =AE_0 sin(\omega t)=\pi r^2 E_0 cos(\omega t) $ where $A$ is the area of the loop, and $r$ is its radius. Thus, $\frac{d\Phi}{dt}=\omega \pi r^2 E_o cos(\omega t)$, giving:
$$2\pi rB = \mu_0\epsilon_o\frac{d\Phi_e}{dt}= \mu_0\epsilon_o \omega \pi r^2 E_o cos(\omega t)$$
and we obtain the final expression for $B$:
$$B=\frac{1}{2} \mu_0 \epsilon_0 \omega r E_0 cos(\omega t)$$
Notice that in these two cases, the line integral wasn't evaluated mathematically, but rather arguments of symmetry (and a good choice of Amperian loop) were used to reduce it to something easier to work with. Hopefully this gives you an idea of how the Ampere-Maxwell law can be used to find the magnitude of the magnetic field at certain places in different situations. 628