Give an example of a property that the Biot-Savart law cannot be used to calculate

The Biot-Savart law cannot be used to determine the intensity of an electric field. 

The Biot-Savart Law determines the magnetic field intensity B near a current-carrying conductor in terms of magnetic field intensity generated by its source current element. Consider a wire carrying an electric current I and also consider an infinitely small length of a wire dl at a distance r from point A

It is clear from the diagram that, Biot-Savart  Law states that magnetic intensity dB at a point A due to current I flowing through a small element dl is,

a) Directly proportional to the current (I).

b) Directly proportional to the length of the element (dl).
c) Directly proportional to the sine of angle θ between the direction of current and the line joining the element dl from point A.

d) Inversely proportional to the square of the distance (x) of point A from the element dl.
$dB \alpha \frac{I dl \sin \theta }{r^2}$
$dB = K \frac{Idl \sin \theta }{r^2}$
$K = \frac{{\mu }_0{\mu }_r}{4\pi }$
${\mu }_0$ = Absolute permittivity of air in a vacuum
${\mu }_r$= relative permittivity.
It is used to determine the strength of the magnetic field. The formula is also utilized to determine the flux density and permeability. 

$B = \mu H$
Biot savart law does not explain electric field intensity because the electric field intensity tells us about the magnitude and direction of the force experienced by the charged particle.