# Ampere’s Circuital Law class 12

Last updated on July 23rd, 2023 at 03:53 pm

This post covers Ampere’s Circuital Law (class 12) with its statement and formula.

Ampere’s Circuital Law in electromagnetism is analogous to Gauss’ Law in electrostatics.

## Ampere’s Circuital Law – statement | state Ampere’s Circuital Law

Ampere’s Circuital Law states that the line integral of the magnetic field B around any ‘closed’ path is equal to μ0 times the net charge I passing through the area enclosed by the path.

## Ampere’s Circuital Law formula

The formula presenting Ampere’s Circuital Law is as follows:

ʃL B. dL = μ0 I

Ampere’s Circuital Law

Here μ0 is the permeability of the free space.

[ Also read: Biot-Savart Law statement, derivation, formula]

## Ampere’s Circuital Law derivation class 12 | Ampere’s Circuital Law from Biot-Savart law (derive or obtain)

Ampere’s circuital law can be described as Biot-Savart law expressed in an alternative way.

Here, we will briefly derive or obtain Ampere’s circuital law from the formula of the magnetic field at a point P due to an infinitely long straight current-carrying conductor (this formula is derived using the Biot-Savart law). So it may be said that we will obtain Ampere’s Circuital Law from Biot – Savart law.

The magnetic field at point P due to an infinitely long straight current-carrying conductor is B = μ0 I / (2πr), where P is a point at a distance r from the conductor.

B (2πr) = μ0 I

B (2πr) is the product of the magnetic field and the circumference of the circle of radius ‘r’ on which the magnetic field is constant.

If L is the perimeter of the closed curve and I is the net current enclosed by the closed curve, then the above equation may be expressed as,