Understanding the Biot-Savart Law: Examining a Quarter Loop Example

[kasse]

I'm trying to understand the Biot-Savart law. Isn't the last calculation wrong here: http://planetphysics.org/encyclopedia/QuarterLoopExampleOfBiotSavartLaw.html

I don't understand why "pi" is in the answer.

 

[michalll]

I think its wrong

 

[kasse]

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!

 

[michalll]

I really don't know your result seems to be correct.

 

[alphysicist]

Hi kasse,

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!

That formula that you used is the magnetic field of a solenoid, and is true when the coil is infinitely long (and is useful when the coil is very long compared to its radius and you are far from the ends).

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?

 

[kasse]

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?

Just multiply the formula with N and y = 0, right?

 

[alphysicist]

That sounds right to me.