Use of Biot-Savart Law for Square Loop

In summary, the conversation is about using the Biot Savart law to find the magnetic field at the center of a square loop. The person asking the question integrated the differential magnetic field element separately for each side and multiplied it by 4 to attain the final equation. They also mention the differential form of the equation for an infinite straight wire.
  • #1
Sekonda
207
0
Hey,

My question concerns the integration of the biot savart law of a differential magnetic field element to find the magnetic field at the center of a square loop. The question is part (c) (using info from (b)) of the image below:

electromagnetism3.png


I want to check if what I did was right, but what I did was to integrate the differential magnetic field element separately for each of the 4 sides, using the fact the angle varies between 45 and -45 degrees for each side. So basically I multiplied the integral of the differential magnetic field by 4 and integrated across the limits of 45 degrees and -45 degrees to attain:

[tex]B=\frac{\sqrt{2}\mu _{0}I}{\pi a}[/tex]

Is this right?

Many thanks for any help/comments!
SK
 
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  • #2
Hey Sekonda! :wink:

Yup, looks ok. :smile:

(btw, [3] is the differential form of the usual (µo/4πa)(sinθ1 - sinθ2), = µo/2πa for an infinite straight wire :wink:)
 
  • #3
Cheers thanks, and so it is; I always miss the ''intricate'' relations between scenario's in electromagnetism.

Thanks again,
SK
 

FAQ: Use of Biot-Savart Law for Square Loop

What is the Biot-Savart Law?

The Biot-Savart Law is a mathematical equation that describes the magnetic field generated by a current-carrying wire or a moving charged particle. It is essential in understanding the behavior of electromagnetism and is used extensively in the field of physics and engineering.

How is the Biot-Savart Law used for a square loop?

The Biot-Savart Law can be applied to a square loop by breaking it down into smaller segments and calculating the magnetic field at a point due to each segment. The total magnetic field at the point will be the vector sum of all the individual fields.

What are the assumptions made when using the Biot-Savart Law?

The Biot-Savart Law assumes that the current is steady, the magnetic field is constant, and the magnetic material is linear. It also assumes that the distance between the point of interest and the current-carrying element is much greater than the size of the element.

Why is the Biot-Savart Law useful?

The Biot-Savart Law is useful because it provides a mathematical description of the magnetic field produced by a current-carrying element. This allows us to calculate the strength and direction of the field at any point in space and is crucial in designing and analyzing electromagnets and other devices that use magnetic fields.

Are there any limitations to the Biot-Savart Law?

Yes, the Biot-Savart Law has limitations. It is only valid for steady currents and does not take into account any time-varying effects. It also does not account for the effects of non-linear magnetic materials. In some cases, it may be more appropriate to use other methods such as Ampere's Law or the Biot-Savart Law modified for non-linear materials.

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