AMPERE’S CIRCUTIAL LAW: -

AMPERE’S CIRCUTIAL LAW: -

            This law states that, “The sum of the scalar product of B and ∆L around a closed path is equal to μ₀ times the total current bounded by the closed path is called Ampere’s circuital law”.

                                    ΣB• ∆L = μ₀I

Ampere observed that the value of B at a particular point “P” due to current carrying conductor is directly proportional to the current passing through the conductor and inversely proportional to the radial distance of point ”P” from the conductor. i.e.                                        I

                                    B ∞ I / r          (1)

For circular Amperian loop the constant of proportionality is μ₀ / 2p,                                      pwhere μ₀ is known as free space permeability and its value is                                                         4p × 10⁻⁷ mA⁻¹. Hence equation (1) becomes

                                    B = (μ₀ / 2p) (I / r) = μ₀I / 2pr

Where 2pr = ∆L (circumference of circle) so above equation becomes

                                    B = μ₀I / ∆L

                        Or        B ∆L = μ₀I                    (2)

Since the lines of B are in circular path so therefore ∆L is parallel to B at each and every point, hence

                                    B∆L = B • ∆L

Therefore equation (2) can also be written as

                                    B • ∆L = μ₀I            (3)

In case of irregular Amperian loop, we divide the whole path into small segments each of length ∆L determine the value of B, take the scalar product of B and ∆L, and add up all the contributions we get         B_i • ∆L_i = μ₀I