Ampere's Law Magnetic Field Due To Straight Conductor

Description:

Consider a long current carrying conductor and a point P at a distance ‘r’ from the conductor.

To find the strength of magnetic field at point P we will follow the following steps:

Consider an Amperean loop

• Taking conductor as axis, such that P is on loop.
• Magnetic field will have a shape of loop.
• Therefore, at every point in the field the angle between the Amperean loop and the magnetic field is zero.1111

Calculating the magnetic field ‘B’

∮ B.dl = B ∮ dl

= B.2πr

Calculating the current through the loop-

Current through the loop = i

Applying Ampere’s law

∮ B.→dl→ = μ₀i

Putting values B.2πr = μi

Hence, strength of magnetic field by straight conductor is-