I have purposefully not written out those arguments since this is the homework forums and may be part of what the OP needs to do. As @vela says, Gauss’ law for magnetic fields also works and I still prefer the pure symmetry arguments.bob012345 said:Please give us that argument? I would be interested. Thanks.
I assume they mean the radial contribution to the line integral is zero. The fact that the dot product is zero does not directly imply that the radial field is zero. This is badly stated. What is the text?vela said:Figure 12.15 The possible components of the magnetic field B due to a current I, which is directed out of the page. The radial component is zero because the angle between the magnetic field and the path is at a right angle.
Yeah, that's what I realized when I read the sentence more carefully after first posting it. In the discussion below the figure in the OpenStax textbook, it's explained how to deduce the radial component vanishes.hutchphd said:I assume they mean the radial contribution to the line integral is zero. The fact that the dot product is zero does not directly imply that the radial field is zero.
Actually, scratch that. I found a hole in that argument. Pure symmetry or using Gauss law for magnetic fields is the way to go.Orodruin said:You can do that, yes. What I was referring to was an argument using Ampere’s law on integral form, which is also possible.
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.hutchphd said:I assume they mean the radial contribution to the line integral is zero. The fact that the dot product is zero does not directly imply that the radial field is zero. This is badly stated. What is the text?
The discussion has been, as I understand it, about how to prove there is no radial component, not that such a radial component exists.annamal said: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.annamal said: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.
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.Orodruin said: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.
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?annamal said: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.annamal said: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.annamal said: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 0annamal said: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.
I would not call symmetry arguments ”esoteric”. Some of them do take time to understand though but the basic principle is very simple.alan123hk said:Maybe some esoteric methods take time to study to understand
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).Orodruin said:Since there seems to be some popular demand for this though, I might summarize in a PF Insight in the future.