Magnetic field generated by an infinitely long current-carrying wire

[bob012345]

I still don't understand how you can have a radial component. I thought the magnetic field was always tangent to a circle around the current.

The discussion has been, as I understand it, about how to prove there is no radial component, not that such a radial component exists.

 

[Orodruin]

I still don't understand how you can have a radial component. I thought the magnetic field was always tangent to a circle around the current.

This is strictly true only for a straight wire.

To also repeat, you need an argument to show that this is the case for the straight wire. The rule you are referring to does not pop out of nowhere - it needs to be motivated and before that has been done you cannot say that it is the case. You are asked to show this. You cannot show something by just saying that it has to be like that. You need an argument.

 

[annamal]

This is strictly true only for a straight wire.

To also repeat, you need an argument to show that this is the case for the straight wire. The rule you are referring to does not pop out of nowhere - it needs to be motivated and before that has been done you cannot say that it is the case. You are asked to show this. You cannot show something by just saying that it has to be like that. You need an argument.

According to my problem in post #1, it is talking about a long straight wire, but yet the solution still considers a radial magnetic field.

 

[Delta2]

According to my problem in post #1, it is talking about a long straight wire, but yet the solution still considers a radial magnetic field.

You can prove that the radial magnetic field is zero, using Gauss's law for magnetic fields. Take as gaussian surface a cylinder with the wire at the cylinder axis. What is the flux of magnetic field through this cylinder and what gauss's law for magnetic fields tell us that it should be equal to?

 

[bob012345]

According to my problem in post #1, it is talking about a long straight wire, but yet the solution still considers a radial magnetic field.

Yes, considers then rejects the radial field.

Again, just because the drawing has a radial field does not mean the book is telling you the solution has a radial field and we have been trying to tell you that is not the case any more than all possible answers on a multiple choice test are all correct simply because they are written down.

 

[Orodruin]

According to my problem in post #1, it is talking about a long straight wire, but yet the solution still considers a radial magnetic field.

The problem is that you know the solution without knowing how to demonstrate that it is the solution. Your argument is referring to it as prior knowledge, but you are not able to demonstrate where that knowledge originated. Just because they have drawn a radial component in the picture does not make it non-zero. It is your job to compute it and thereby conclude that it is zero from first principles rather than by adherence to dogma.

 

[alan123hk]

According to my problem in post #1, it is talking about a long straight wire, but yet the solution still considers a radial magnetic field.

Without a doubt, $B_r$ must be equal to 0
Maybe some esoteric methods take time to study to understand
But as mentioned in the post above, there is a relatively simple method that can be used, the Gaussian law of magnetism and the principle of symmetry.

I removed the original attached image as it might not be appropriate in this homework help discussion forum.

 

[Orodruin]

Maybe some esoteric methods take time to study to understand

I would not call symmetry arguments ”esoteric”. Some of them do take time to understand though but the basic principle is very simple.

 

[Orodruin]

Since there seems to be some popular demand for this though, I might summarize in a PF Insight in the future.

Said and done. This summarizes the necessary background of pseudo vectors vs vectors, discusses why the magnetic field is a pseudo vector, and uses a reflection symmetry to conclude that the components along the wire and in the radial direction are equal to zero (you don’t even need the other symmetries of the wire to conclude this - you do need them to conclude that the strength only depends on the distance from the wire).

https://www.physicsforums.com/insights/symmetry-arguments-and-the-infinite-wire-with-a-current/