Magnetic field at center of loop

In summary, the magnetic field at the center of the loop in the figure is incorrect because the field is calculated for a straight conductor and a circular current loop, when in reality only the straight part of the wire is present.
  • #1
Linus Pauling
190
0
1. What is the magnetic field at the center of the loop in the figure ?

knight_Figure_32_54.jpg




2. Ampere's Law



3. If the surface integral of B*ds = Bl = 2*pi*d = u0*I:

B = u0I / (2pi*d) = 5*5-5 T, which is wrong.
 
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  • #2
B = u0I / (2pi*d)
This formula is for a long straight conductor.
In the given problem in addition to the straight conductor, one circular loop is also present.
Find the field at the center of the circular coil and add it to the above.
 
  • #3
Still not getting it.

I calculated B_loop = u0IR2/[2(z2+R2)3/2]

With z = 0 because we're at the center of the loop, it reduces to B = u0I/2R = 3.15*10-4.

Adding that to my first answer yields 3.65*10-4
 
  • #4
I know the answer is 4.14*10-4 so I muse be making some sort of small calculation error...
 
  • #5
Could somebody also explain, conceptually, why I would calculate B for a straight conductor and a loop and add them? For example, why would I calculate B for the full length of the conductor if some of it isn't straight (i.e. is looped)? Or is that part of my mistake here?
 
  • #6

B = u0I / (2pi*d) = 5*5-5 T
Check this calculation. Here d = 1 cm.
 
  • #7
why is d = 1cm and not 2cm? Is it the radius of the loop? Why not call it r?
 
  • #8
d is the distance from the straight wire, which is 1 cm.
 
  • #9
Linus Pauling said:
Could somebody also explain, conceptually, why I would calculate B for a straight conductor and a loop and add them? For example, why would I calculate B for the full length of the conductor if some of it isn't straight (i.e. is looped)? Or is that part of my mistake here?

Suppose that you could see the electrons flowing. The straight part of the wire in this problem looks exactly like a normal straight wire: the electrons are flowing in a straight line from one end to the other. The circular part looks exactly like a normal circular current loop: the electrons seem to be going in circles. Due to the principle of superposition, you can calculate the magnetic field induced by the straight part and the circular part and add them to get the resultant field.
 
  • #10
Thanks
 

FAQ: Magnetic field at center of loop

What is the magnetic field at the center of a loop?

The magnetic field at the center of a loop is the magnetic field strength at the center point within a circular loop of current.

How is the magnetic field at the center of a loop calculated?

The magnetic field at the center of a loop can be calculated using the equation B = μ0I/2r, where B is the magnetic field strength, μ0 is the permeability of free space, I is the current flowing through the loop, and r is the radius of the loop.

Does the magnetic field at the center of a loop depend on the orientation of the loop?

Yes, the magnetic field at the center of a loop is affected by the orientation of the loop. If the loop is placed perpendicular to the magnetic field, the magnetic field at the center will be at its maximum strength. If the loop is parallel to the magnetic field, the magnetic field at the center will be zero.

What factors affect the magnetic field at the center of a loop?

The magnetic field at the center of a loop is affected by the current flowing through the loop, the size of the loop, and the distance between the center of the loop and the point where the magnetic field is being measured. It is also affected by the orientation of the loop and the strength of the external magnetic field.

Why is the magnetic field at the center of a loop important?

The magnetic field at the center of a loop is important in many applications, such as in electromagnets, motors, and generators. It also helps to understand the behavior of magnetic fields in different orientations and the interaction between magnetic fields and currents.

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