Discuss the similarities and differences between the Biot-Savart law and Coulomb's law.

(N/A) Similarities and differences between the Biot-Savart law and Coulomb's law are as follows:
Similarities:
$(1)$ Both obey the inverse square law with respect to distance $(1/r^2)$.
$(2)$ Both are long-range forces/fields.
$(3)$ The principle of superposition applies to both fields.
For the static electric field, $E = \frac{kQ}{r^2}$, so $E \propto Q$.
Similarly, for the Biot-Savart law, $B = \frac{\mu_0}{4\pi} \frac{Idl \times \hat{r}}{r^2}$, so $B \propto Idl$.
Differences:
$(1)$ The magnetic field is produced by a vector source $(Id\vec{l})$, whereas the electric field is produced by a scalar source $(dq)$.
$(2)$ The electrostatic field is directed along the displacement vector $\vec{r}$ joining the source and the field point. In contrast, the magnetic field is perpendicular to the plane containing both the current element $Id\vec{l}$ and the displacement vector $\vec{r}$.
$(3)$ The Biot-Savart law depends on the angle $\theta$ between the current element and the position vector $(\sin \theta)$. For $\theta = 0^{\circ}$, the magnetic field is zero along the axis of the current element. Conversely, Coulomb's law does not depend on any angle $\theta$.