The discussion revolves around understanding the Biot-Savart law, particularly in the context of a quarter loop and a short coil with multiple loops. Participants are examining specific calculations and expressions related to magnetic fields generated by these configurations.
The discussion is active, with participants sharing their interpretations and calculations. Some guidance has been offered regarding the application of formulas for magnetic fields in short coils, and there is an exploration of how to approach the problem of finding the magnetic field at the center of the coil.
Participants are working under the constraints of homework assignments, which may limit the information available for discussion. There is an emphasis on understanding the assumptions behind the formulas used, particularly regarding the length of the coil in relation to its radius.
kasse said:I also have a problem with this task:
http://www.badongo.com/pic/3641364
In a) I'm asked to show that the expression for B in P is correct, which I have made.
In b) the loop is replaced by a short coil with N loops. The direction of the current is the same. I'm asked to find
- the magnetic field in the center of the coil, and
- in what distance along the y-axis from the center of the coil is the B field reduced to 1/3 of it's maximal.
I use this formula to find the magnetic field in the center: B*L = N*(mju)*I --> B = N*(mju)*I/L
The answer is the same as in my book, except that L is replaced with 2R. Why is this? If the coil is short, it's length should definitely not be 2L!
alphysicist said:Hi kasse,
Here you want to think of the coils as being so short that the coils are effectively on top of one another. You can find the field of one loop at its center by using the result from part a; what is the value of y at the center of the loop? Then the magnetic field of N loops would just add together. Do you get the result?