Ampere's Law Magnetic Field due to Current In Cylinder

Description:

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

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

• P is outside the conductor at distance ‘r’

  Draw the Amperean loop in shape of co-axial circle or radius r. Magnetic field is also circular in direction and same at every point.

  θ = 0 (B→dl→)

  ∮ B.→dl→ = ∮ B.dlcosθ =  B ∮ dl

  = B2πr

• Calculating the current through the loop-

  Current through the loop = i

• Applying Ampere’s law

  ∮ B.→dl→ = μ₀i

  Putting values B2πr = μ₀i

  Hence, strength of magnetic field due to cylindrical conductor is-

  B_out =

  μ₀i/2πr
  B_surface =

  μ₀i/2πR
  B_in =

  μ₀i/2πR²

  r

  B at centre is zero.