Biot Savart's Law and Equation
Biot-Savart Law:
Biot-Savart law was discovered in 1820 by two physicists Jeans-Baptiste Biot and Felix Savart. According to this law:
From equation $(1)$,$(2)$,$(3)$,$(4)$ :
$\qquad dB \propto \frac{i dl sin\theta}{r^{2}}$
Now replace the proportional sign with the constant i.e. $\frac{\mu_{0}}{4 \pi}$. Therefore the above given equation can be written as
$ dB = \frac{\mu_{0}}{4 \pi} \frac{i dl sin\theta}{r^{2}}$
The magnetic field at point $P$ due to entire conductor:-
$ B =\frac{\mu_{0}}{4 \pi} \int \frac{i dl sin\theta}{r^{2}}$
Case$(1)$: If $\theta=0^{\circ}$ then the magnetic field will be zero from the above equation i.e.
$B=0$
Case$(2)$: If $\theta=90^{\circ}$ then the magnetic field will be maximum from the above equation i.e.
$B =\frac{\mu_{0}}{4 \pi} \int \frac{i dl}{r^{2}}$.
The vector form of Biot-Savart magnetic field equation is:-
$ \overrightarrow{B} =\frac{\mu_{0} i}{4 \pi} \int \frac{ \overrightarrow{dl} \times \overrightarrow{r}}{r^{3}}$
- The magnetic field is directly proportional to the length of the current element.
$dB \propto dl \qquad (1)$
- The magnetic field is directly proportional to the current flowing in the conductor.
$dB \propto i \qquad (2)$
- The magnetic field is inversely proportional to the square of the distance between length of the current element $dl$ and point $P$ (This is that point where the magnetic field has to calculate).
$dB \propto \frac{1}{r^{2}} \qquad (3)$
- The magnetic field is directly proportional to the angle of sine. This angle is the angle between the length of the current element $dl$ and the line joining to the length of the current element $dl$ and point $P$.
$dB \propto sin\theta \qquad (4)$
