Find the magnetic field due to a long straight conductor using Ampere’s circuital law.
Answers
Consider a straight conductor of infinite length carrying current I and the direction of magnetic field lines. Since the wire is geometrically cylindrical in shape C and symmetrical about its axis, we construct an Amperian loop in the form of a circular shape at a distance r from the centre of the conductor. From the Ampere’s law, we get Where dl is the line element along the amperian loop (tangent to the circular loop). Hence, the angle between magnetic field vector and line element is zero. Therefore, where I is the current enclosed by the Amperian loop. Due to the symmetry, the magnitude of the magnetic field is uniform over the Amperian loop, we can take B out of the integration. For a circular loop, the circumference is 2πr, which implies, Where n^n^ is the unit vector along the tangent to the Amperian loop. This perfectly agrees with the result obtained from Biot-Savarf s law as given in equation B⃗ B→ = μ0I2πaμ0I2πan^n^ -magnetic-induction-due-to-a-long-straight-conductor-using-amperes-circuital-law