# Calculating Magnetic Field of Square Loop: Questions Answered!

• Planck const
In summary, the conversation discusses the use of Biot-Savart law in a system with a square loop and the appropriate use of cos or sin in the equation. The suggestion is to remember the cross product form of the law and to draw a diagram for a better understanding. The summary concludes with a reminder that the magnetic field is related to the cross product of the current element and the directional vector.
Planck const
OK...
My question is, if I have so system like square loop... and all the donations be summed up by Bcos(Tetha) or sin(Tetha), am I need to multiply the cos/sin in Biot -Savart rule?
So I will get
dB=const*dx * sinTetha*cosTetha / r^2
or I just need to exchange cos with sin? (if all donations are summed up with BcosTetha)

?​

Thanks for watchers and answerers !

My suggestion is its always better to go down to the basics and instead of remembering the cos(theta) form of Biot-Savart law, instead remember its CROSS PRODUCT form, that way u'd always know how to approach.
simply draw the figure check the direction and proceed, its absolutely simple if done the right way.

You are not answering me. If someone ask A or B, you need to say - A or B

I didn't understand - with cos or withnt?

Vipuldce already answered your question. I'm not going to attempt because I still do not understand your thinking here but such misunderstandings are trivial if you just go back to the original equation. The magnetic field is related to the cross product of the current element and the directional vector from your current element to the observation point.

Drawing a simple diagram and giving it some thought should clear things up for you.

Hello! Thank you for your question. Based on the information provided, it seems like you are trying to calculate the magnetic field of a square loop using the Biot-Savart law. In this case, you do not need to multiply the cosine or sine functions in the equation. The Biot-Savart law already takes into account the angle between the current element and the distance from the point of interest. So, your equation would be:

dB = const * dx / r^2

Where dx is the current element and r is the distance from the point of interest. This equation holds true for all angles, whether they are summed up with cosine or sine. I hope this helps clarify your question. Happy researching!

## 1. How do you calculate the magnetic field of a square loop?

To calculate the magnetic field of a square loop, you can use the formula: B = μ₀I/2r, where B is the magnetic field, μ₀ is the permeability of free space, I is the current flowing through the loop, and r is the distance from the center of the loop to the point where you want to calculate the field.

## 2. What is the direction of the magnetic field at the center of a square loop?

The direction of the magnetic field at the center of a square loop is perpendicular to the plane of the loop. This means that the field lines are pointing out of the loop on one side and into the loop on the other side.

## 3. How does the magnetic field change as you move away from the center of a square loop?

The magnetic field decreases as you move away from the center of a square loop. This is because the distance (r) in the formula for calculating the field is in the denominator, meaning that as r increases, the field decreases.

## 4. Can the magnetic field of a square loop be affected by changing the current or size of the loop?

Yes, the magnetic field of a square loop can be affected by changing the current or size of the loop. Increasing the current will increase the field, while increasing the size of the loop will decrease the field. This is because both of these factors are directly related to the B = μ₀I/2r formula.

## 5. How is the magnetic field of a square loop affected by the presence of other magnetic fields?

The magnetic field of a square loop can be affected by the presence of other magnetic fields. If the other field is parallel to the loop, it will add to the field already present. If the other field is perpendicular to the loop, it will cause the field lines to bend and can result in a net zero field at certain points. This is known as the superposition principle.

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