# 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 statesthat the line integral of the magnetic fieldBaround any ‘closed’ path is equal to μ_{0}times the net chargeIpassing through the area enclosed by the path.

## Ampere’s Circuital Law formula

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

ʃ

_{L}B. dL= μ_{0}IAmpere’s Circuital Law

Here μ_{0} 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 = μ_{0} I / (2πr), where P is a point at a distance r from the conductor.

B (2πr) = μ_{0} 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,

BL = μ_{0}I

In a more generalized way, Ampere’s circuital law is written as ʃ_{L} **B**. d**L** = μ_{0} I

The line integral does not depend on the shape of the path or the position of the wire within the magnetic field. If the current in the wire is in the opposite direction, the integral would have the opposite sign.

If the closed path does not encircle the wire (if a wire lies outside the path), the line integral of the field of that wire is zero.

Although derived for the case of a number of long straight parallel conductors, the law is true for conductors and paths of any shape.