Magnetic Field in a Solenoid

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Homework Statement

Explain why the contribution of B°dl of the magnetic field at sections b and d of the enclosure length must be zero, even inside the solenoid.

Homework Equations

Ampere's Law: ∮ B dl= U_0 I_enclosed N

The Attempt at a Solution

The right and left sides of the loop have a magnetic field that is perpendicular to the solenoid loop. Because of this, it makes no contribution to the circulation B°dl there.

 

[Abhishekdas]

Hi SgtMousse ...

Observe that all the circles in your diagram which reprsent the wires form a solenoid with current in a direction into the plane .Now you must be knowing that the solenoid is infinitely long right? In such a case the components of magnetic field due to the wires which are parallel to the axis of the solenoid add up and all others cancel out...Thus you are left with a uniform (almost uniform if you neglect the edges of the solenoid) magnetic field inside the solenoid parallel to the axis and in this case parallele to the side c... Now in the sections 'b' and 'd' the 'dl' is perpendicular to the magnetic field (which is along the direction of c)... So in those two sides even inside the solenoid B.dl is 0...

Hope you got this clear now...