Biot-Savart Law and its Application to Find Magnetic Field on The Axis and at The Center of A Current Carrying Circular Loop

Biot-Savart Law

Biot-Savart law gives the magnetic field at a point due to a small current element.

Mathematically,

dB = \frac{\mu_{0}}{4\Pi}.\frac{Idl.\sin\Theta}{r^{2}}

Here,

dB = Small magnetic field intensity

$\frac{\mu_{0}}{4\Pi}$ = Constant

I = Net current

dl = Elementary length on loop

r = Radius of loop

Consider a circular coil or loop of radius “r” carrying current I.

Let’s consider an element of the coil XY of length $dl$ .

Now magnetic field intensity at the center “O” due to current element $Idl$ is dB.

Then according to Biot-Savart’s law,

dB = \frac{\mu_{0}}{4\Pi}.\frac{Idl.\sin\Theta}{r^{2}}....... (1)

Where,

$\Theta$ = Angle between $\overrightarrow{dl}$ and $\overrightarrow{r}$ .

In case of circular loop, $\Theta$ = ${90^{0}}$