Magnetic Field Due to Straight Current Carrying Conductor

Description:

Straight current carrying conductor of finite length –

Suppose a straight current carrying wire AB, carrying current i, lies in the plane of the paper as shown in the figure, P is a point at a perpendicular distance R from conductor, where magnetic field is to be determined.

According to Biot-Savart’s Law, the field at point P due to current element idl = qVB→ is

Now from the figure dlsinθ = rdφ and cosφ = R/r

Hence magnetic field due to the whole conductor

Straight current carrying conductor of infinite length –

θ₁ = θ₂ = π/2

Magnetic field on perpendicular bisector of a conductor of finite length –

Where,

𝑎 = Length of the wire.

𝑑 = Perpendicular distance of the point P.

Magnetic field at point exactly in front of the end of a semi-infinite wire –

θ₁ = 0 and θ₂ = π/2

Magnetic field at a point not exactly in front of the end of a semi-infinite wire –

θ₁ = α and θ₂ = π/2