Question

Give a Qualitative discussion of the magnetic field produced by a straight solenoid.Apply Amper

Answer 1

A solenoid means an insulated copper wire wound closely in the form of a helix 

Calculation of magnetic field inside a long straight solenoid:

        The magnetic field inside a closely wound long solenoid is uniform everywhere and zero outside it.The figure shows the sectional views of solenoid. 

At various turns of solenoid,current comes out of the plane of paper at points marked as .To determine the magnetic field B→B→ at any inside point,consider a rectangular closed path abcdabcd as the amperean loop.According to Ampere’s circuital law,

  

   ∲B→.dl→∲B→.dl→ 

             =μ0×=μ0× Total current through the loop abcdabcd 

Now  ∲B→.dl→=∫baB→.dl→+∫cbB→.dl→+∫dcB→.dl→+∫adB→.dl→∲B→.dl→=∫abB→.dl→+∫bcB→.dl→+∫cdB→.dl→+∫daB→.dl→  

But 

∫cbB→.dl→=∫cbBdl∫bcB→.dl→=∫bcBdl cos900=0cos⁡900=0 

∫adB→.dl→=∫adBdlcos900=0∫daB→.dl→=∫daBdlcos⁡900=0 

∫dcB→.dl→=0<