Calculation of the magnetic field of four quarter circles

[katarameno]

Homework Statement

Calculate the magnetic field that four quarter circles produce . The The quarter circles are equidistant from each other by 50 mm and are located at the vertices of a square. The current is 1 A, and the radius of each quarter circle is 10 mm.Also, determine the direction of the magnetic flux lines.

Relevant Equations

Bio-Savart Law for current loop

The diagram is something like this, and I want to calculate the magnetic field at the center using the Biot-Savart law. In this case, do the magnetic fields formed by the quarter circles pairwise alternate with each other?

 

[Gordianus]

Please, show us your attempt.

 

[Gordianus]

You haven't how current flows. Anyway, the B's can't lie on the plane

 

[katarameno]

yes sorry , I have no idea how to calculate this , can you help me ?

 

[katarameno]

Consider that the current flows anticlockwise in each loop

 

[Aurelius120]

Where do we have to calculate the field ?

 

[katarameno]

at the center of all the quarters

 

[Gordianus]

Try to write Biot's law for just one quarter but do not integrate yet.

 

[Steve4Physics]

Hi @katarameno. Welcome to PF. As you've probably already realised, the forum rules mean we don't solve problems for you; we try to guide you to do it for yourself. Forum rules are here.

IMO the problem is pretty difficult and is not suitable for someone who isn't already confident with simpler Biot-Savart problems, So when you say

I have no idea how to calculate this

that's worrying.

What course/level are you? Have you done other (simpler) Biot-Savart problems?

And are you certain that you have the current directions correct - all anticlockwise?

If you aren't familiar with using the Biot-Savart law, look at some worked problems. For example finding the field due to a square loop is explained in this video. You need at least that level of knowledge to tackle your problem.

 

[Aurelius120]

IMO the problem is pretty difficult and is not suitable for someone who isn't already confident with simpler Biot-Savart problems, So when you say

But now that the question has been asked,
Is it even possible to solve this by using only Biot-Savarts Law and Ampere's Circuital Law?

 

[Steve4Physics]

But now that the question has been asked,
Is it even possible to solve this by using only Biot-Savarts Law and Ampere's Circuital Law?

It's certainly possible in principle with the Biot-Savart law. But I suspect something messy like an elliptic integral or numerical integration. would be needed. If so, the problem is unsuitable for a student meeting the Biot-Savart law for the first time - which, from the OP's posts, sounds like like the situation.

 

[Aurelius120]

It's certainly possible in principle with the Biot-Savart law. But I suspect something messy like an elliptic integral or numerical integration. would be needed. If so, the problem is unsuitable for a student meeting the Biot-Savart law for the first time - which, from the OP's posts, sounds like like the situation.

So more of a maths question than a physics one?

 

[Steve4Physics]

So more of a maths question than a physics one?

Can't really answer that! Maybe it's better to think holistically - dealing with the maths is an essential part of the process of doing physics.