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Question
Using Ampere’s circuital law, obtain the expression for the magnetic field due to a long solenoid at a point inside the solenoid on its axis ?
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Solution
Solenoid
• It consists of an insulating long wire closely wound in the form of helix.
• Its length is large as compared to its diameter.
• Magnetic field due to RQ and SP path is zero because they are perpendicular to the axis of solenoid. Since SR is outside the solenoid, the magnetic field is zero.
• The line integral of magnetic field induction `vecB` over the closed path PQRS is
`oint_(PQRS) vecB*vecdl =oint_(PQ)vecB*vecdl =BL`
From Ampere’s circuital law,
`oint_(PQRS)vecB*vecdl = mu_0 `× Total current through rectangle PQRS
BL = μ0 × Number of turns in rectangle × Current
BL = μ0nLI
∴ B= μ0nI
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