The net magnetic field at the center

In summary, the conversation discusses the direction and magnitude of magnetic fields and the struggle to find a correct answer. The speaker suggests drawing the arrows again and extending the lines to the center, ultimately leading to a correct solution.
  • #1
PhysicsTest
238
26
Homework Statement
Four, long, parallel power lines each carry 100-A currents. A cross-sectional diagram of these lines is a square, 20.0 cm on each side. For each of the three cases shown in , calculate the magnetic field at the center of the square.
Relevant Equations
##B = \frac {\mu_0 I} {2a}##
The current direction is as follows
1601316385651.png

I think so much and do the right hand rule i get 0 at the center, but not sure why the answer is non zero. I have shown the directions of the magnetic fields, i have not shown the magnitudes of equal length but they all are equal. Why the answer is non zero, what mistake i am doing?

1601316443107.png
 
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  • #2
I see only one case ? Mixup of answers ?
 
  • #3
BvU said:
I see only one case ? Mixup of answers ?
The first two I could solve, this is the 3rd one which I am struggling to get answer.
 
  • #4
May I suggest drawing the arrows again?
 
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Likes BvU
  • #5
Gordianus said:
May I suggest drawing the arrows again?
I end up getting below the same,

1601320343395.png
 
  • #6
No, try again.
 
  • #7
Gordianus said:
No, try again.
Ok, chances are there of a below diagram
1601321196983.png

But a very tough one to know where it will be left. Am i correct here?
 
  • #8
Try drawing the B-lines of each wire
 
  • #9
Gordianus said:
Try drawing the B-lines of each wire
The B lines are like this
1601322227148.png

Everything seems to be left.
 
  • #10
Good! Now extend the lines to the center and draw the arrows again.
 
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Likes hutchphd
  • #11
1601324249923.png

Surely the tougher than i expected. Hope it is correct.
 
  • #12
Victory!
 
  • Like
Likes PhysicsTest
  • #13
Thank you very much for support.
 

Related to The net magnetic field at the center

1. What is the definition of the net magnetic field at the center?

The net magnetic field at the center is the total magnetic field at the exact center point of a magnet or magnetic object. This point is often referred to as the magnetic pole.

2. How is the net magnetic field at the center calculated?

The net magnetic field at the center is calculated by adding up the individual magnetic fields from all the tiny magnetic domains within the magnet or object. This can be done using mathematical equations or by using a magnetometer to measure the field directly.

3. What factors affect the strength of the net magnetic field at the center?

The strength of the net magnetic field at the center is affected by the size and shape of the magnet or object, the strength of the individual magnetic domains, and the distance from the center point.

4. Can the net magnetic field at the center be manipulated or changed?

Yes, the net magnetic field at the center can be manipulated or changed by altering the strength of the individual magnetic domains, changing the orientation of the magnet or object, or by introducing other magnetic fields that can either reinforce or cancel out the net field.

5. Why is the net magnetic field at the center important?

The net magnetic field at the center is important because it is the primary factor that determines the behavior of a magnet or magnetic object. It is also crucial in understanding and predicting the interactions between different magnets or objects with magnetic properties.

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