Magnetic field in rectangular coil (not solenoid) Amperes law

[LambertoPierto]

Homework Statement

I have a rectangular coil with length L and the cross-section's sides has length a and b (b>a). A wire is tightly wrapped around N times. Calculate the magnetic field inside the coil.

Homework Equations

The problem I have is that in class we were taught how to calculate the magnetic field for a solenoid were the diameter is much smaller than the length of the soleind, making the magnetic field inside almost constant. We used Ampere's law. Since I now have a rectangular coil I'm confused.

The Attempt at a Solution

If I were to use the same approach as for a solenoid I would draw a rectangular path parallell to the magnetic field inside the coil. I would traverse the path counterclockwise and everytime I wire passes through my rectangular loop I would add the magnetic field times the length of the side parallell to the magnetic field. If I then would go on the result would be the same as for the solenoid, that can't be right?

But then again, if I divide every loop of the wire around the coil into indivdiual cases and then add up all the N loops. Then I could safely assume that the magnetic field is constant right!? And if I proceeded with making a rectangular path and calcualte the magnetic field using Ampere's law. Wouldn't I just end up with the same result as for the soleind? But then why were the professor implying so strongly that the solenoid had to have a small diameter. Aswell dose the length of the sides, a and be, truly not contribute? I would highly appreciate any nod in the right direction for solving this!

 

[mukul]

yes the result will come out to be same as that in case of solenoid provided the length of rectangular coil is >> than width of rectangular coil.

this >> condition is needed in both the case (ie rectangular coil case and solenoid case) since this is the condition which allows us to assume that magnetic field inside the element is only in direction of length of element. In reality, the magnetic field at the edges is little towards outward away from center.

 

[LambertoPierto]

yes the result will come out to be same as that in case of solenoid provided the length of rectangular coil is >> than width of rectangular coil.

this >> condition is needed in both the case (ie rectangular coil case and solenoid case) since this is the condition which allows us to assume that magnetic field inside the element is only in direction of length of element. In reality, the magnetic field at the edges is little towards outward away from center.

View attachment 97571

Thank you!

 

[mukul]

Thank you!

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