**Magnetic Field Due to a Cylindrical
Wire**

Magnetic field due to a cylindrical wire is obtained by the application of Ampere’s law.

**1) Outside the Cylinder:**

In all above cases magnetic field outside the wire at P, ∫B̄.dl̄̄ = µ₀I ⇒ B ∫dl = µ₀i.

B x 2πr = µ₀i ⇒ B_{out} = µ₀i/ 2πr

In all the above cases, B_{surface}
= µ₀i/ 2πR

**2) Inside the hollow cylinder: **Magnetic field inside the
hollow cylinder is zero.

**3) Inside the solid cylinder: **Current enclosed by loop
(I) is lesser than the total current.

Current density is uniform, i.e. J =
J ⇒ i’ = i x (A’ x A) = i (r²/R²),
hence at inside point ∫B̄_{in}.dl̄ = µ₀’ ⇒ B = µ₀ir/ 2πR².

**4) Inside the thick portion of hollow
cylinder: **Current
enclosed by loop is given by as, i’ = i x (A’/ A) = i x [(r² – R₁²)/ (R₂² – R₁²)]