# Which angle should it be?

in the formula

$$dB = \frac{\mu_0l ~|dl \times r|}{4 \pi r^3}$$

and the image

where dl is in y-z plane and dB is in x-y plane. the ring conductor is in y-z plane carrying current I in direction as mentioned
EDIT: also point p can move in the circular ring

EDIT 2:To clear the confusion...The dl vector is having (L alphabet) and current is I (i alphabet).

I want to know that is the angle between dl and r is 'Theta' ? how?

• are you claiming that $\theta$ is the angle between $dI$ and $r$? Commented Mar 1, 2014 at 16:10
• No, but I want to confirm that...because it is given in my text book and i cannot understand how ? Commented Mar 1, 2014 at 16:14
• is $dI$ parallel to z-axis and perpendicular to y-axis? Commented Mar 1, 2014 at 16:18
• No, not always because point p is arbitrary point on that circular conductor Commented Mar 1, 2014 at 16:19

Angle between $dl$ and $r$ at any point on the circular loop is $90^0$. Look at the below figure.

• Which software is used to make such figures? Commented Mar 1, 2014 at 20:21

the angle between $dl$ and $r$ is $\pi/2$, which is not $\theta$.

$\theta$ is the angle between $r$ and y-z plane. if you know what is $x$ and $r$, then $\sin\theta=x/r$, where $x$ is the distance from the origin to the point of intersection of $r$ and x-axis, and $r$ is the distance from p point to the same place

UPDATE. $\theta$ is important because your $dB$ is at this angle to x-axis. so when you add up all $dB$ resulting from all points p, only the $\cos\theta dB$ parts will contribute, because the part of $dB$ which is in y-z plan will cancel each other. for each point p, there's is an opposite point on the ring, they cancel each other's $dB$ on y-z plane, but not on x-axis. that's why resulting $B$ will be on x-axis.

• So, according to you x/r is constant ? let me update the image Commented Mar 1, 2014 at 16:29
• what do you mean by constant? it is constant regardless which point p you choose. it is not constant with regards to which point on x-axis you're considering Commented Mar 1, 2014 at 16:30
• Fix this answer because the angle is (pie)/2 and not (pie)/4 Commented Mar 1, 2014 at 17:00
• @MukulKumar, good catch Commented Mar 1, 2014 at 17:01
• $\pi$ is 180, so 90 is $\pi/2$ Commented Mar 1, 2014 at 17:48

The angle between $\vec {dl}$ and $\vec r$ is $2n\pi \pm\dfrac{\pi}{2}$ because the angle between them is the angle between the x-r plane and y-z plane.

• Please reconsider the question Commented Mar 1, 2014 at 16:12
• The vector r only stays in x-y plain in two cases in rest cases the vector shifts away(in four octants of graph where x is positive) hence the angle is not what you are saying Commented Mar 1, 2014 at 16:23
• The point p is not on y-axis but is on the circle (arbitrary).That is why the angle is not (never) a constant but a variable Commented Mar 1, 2014 at 16:41
• I understood now.Looks like I got a problem of 3D imagination. Commented Mar 1, 2014 at 16:47
• @MukulKumar Ask for a mathematical prove in your question. you will get a nice answer. Btw choose the most appropriate anwser as accepted cya. Commented Mar 1, 2014 at 16:50