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,

Here,

dB = Small magnetic field intensity

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

I = Net current

dl = Elementary length on loop

r = Radius of loop

Biot-Savart Law – Application to Find Magnetic Field on The Center of A Current Carrying Circular 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,

Where,

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

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