# Confusion in reaction force of Ampere's Force Law [closed]

I am reading Maxwell's "A Treatise on Electricity and Magnetism" and I have some confusion in the following pages:

The element ds is resolved into its components $\alpha$ and $\beta$;and the element ds' is resolved into its components $\alpha'$, $\beta'$ and $\gamma'$. In pages 153 & 154, Maxwell discusses the forces between the components $\alpha$ and $\beta$ on one hand and $\alpha'$, $\beta'$ and $\gamma'$ on the other.

Now onto the main question:

There is an equal and opposite force between each components of elements ds and ds'. For example, for a force on $\alpha$ due to $\beta'$, there is an equal and opposite force on $\beta'$ due to $\alpha$.This is illustrated in the image below:

$$\text{In the image:}\\ \vec{R_{F}}= \text{resultant force}\\ \vec{F}=\text{force component}$$

Now, how come Maxwell say in page 161, Article 527 "Of these four different assumptions that of Ampere is undoubtedly the best, since it is the only one which makes the forces on the two elements not only equal and opposite but in the straight line which joins them."

According to me, there would be an equal and opposite force in all four cases. This is because there is an equal and opposite force between each components of elements ds and ds'. Hence, there would be an equal and opposite force between elements ds and ds'.

I think I might be somewhere wrong in my question. That is why I end up getting the wrong conclusion,i.e.there would be an equal and opposite force in all four cases. I need the answerer to point out where I am wrong.

• This is a completely reasonable question and is in detail. Why is it put on hold? Please remove this question from hold. – N.G.Tyson Jun 28 '16 at 5:46
• One suggestion for you would be that you summarize the quoted text. If people have to read a long treatise before they can answer why something isn't the way you think it should be, then most people would likely opt to not answer the question at all – Jim Jun 28 '16 at 12:58
• I summarised most of the quoted text nicely in a table chart. I also uploaded the pages so as to show the reader clearly what is written in the text. – N.G.Tyson Jun 28 '16 at 14:28