Magnetic Filed Due to Solenoid

Description:

A solenoid is a long cylindrical helix, which is obtained by winding closely a large number of turns of insulated copper wire over a tube of cardboard or china clay. When electric current is passed through it, a magnetic field is produced around and within the solenoid.

Consider a rectangular Amperean loop PQRS. Along PQ the field is zero. Along transverse sections PS and QR, the field component is zero. Let the magnetic field along SR be B.

∮ Bdl cosθ = μ₀i

∮ B→dl→ = ∮ Bdl cosθ

= R∫S Bdl cos0 + Q∫R Bdl cos90^o + P∫Q Bdl cos180 + S∫P Bdl cos90^o

= B R∫S dl + 0 + 0 + 0 = Bl

Current passing through loop – 𝒏𝒍𝒊

Thus, the number of turns per unit length is ‘n’, then the total number of turns is ‘nh’. The enclosed current is I_e = I(𝑛ℎ) where I is the current in the solenoid.

From Ampere’s circuit law

BL = μ₀I_e, Bh = μ₀I(nh)

B = μ₀nI

The direction of the field is given by the right-hand rule. The solenoid is commonly used to obtain a uniform magnetic field.