i just want to understand the integration process so just the math is what i want to understand. The problem is that I have a three dimensional field in which a semicircle lies in the x plane in which current travels. In the y plane there is a magnetic field (B) coming up out of the semicircle and it doesnt say how long (Question about that in a sec). The problem wanted to know what the cross product of these two is. So I took it at the axis and integrated with respect to sin theta because that what a cross product is. I(current) times B(magnetic field) times the sin of the angle between them. I took just half of the semicirlce and integrated sin from 0 to 90 degress and then multiplied my final answer by 2 because of symmetry. Ok a few confusing things about this problem. I integrated from the axis in essence to you the symmtry to help me but the problem i see with this is that treating the magnetic field to be just at the origin but there are N amoun of field lines. So infinite lines that i must sum via integration, but how like i have thought about this all day and no matter how i integrate it it doesnt pan out because if i integrate from 0 90 for the bottom lines it doesnt help with other ones that aren't lying on the axis cause they have 360 degrees around them. I hope this is making sense a simple drawing well cover it very easily. Second problem was how we integrate with respect. As i was doing the problem i pictured this magnetic field to be short in lenth therefore sin would work but then i pictured it to be very long maybe even assumed to be infinite than i said sin would turn to cos and integrated with respect to cos theta but for both answers i got the same thing a negative answer which is fine but i just dont understand how to do the math it's complex to me. and to finish the problem after i integrated and was done i just multiplied the answer by N amount of lines. but i know that how you integrate one of the many N's is not the same as how you should integrate another N. It to me is like looking at a map of the United states and trying to take each mountain and some up the weight of the rock or material. You can't treat it as amorphic with smoothness each case of mountain is differnt each is a diffent height and you would have to integrate each one then sum up all that are in the US. It's almost as if you integrate and then have to integrate again but can't. My thoughts are that if you have a semicircle and you have 5 random dots and you need to integrate them with respect to angle how do you treat them as a system or can you not because what you do to one will not help with the others(example if a dot lie on the very bottom of the semicircle all you could do is go pi around and you are done but go up just a lil to the next dot and it have 2pi around but alot more up then down. I hope all this made sense and forget the physics this problem could be one of amillion situations you've seen not just cross products of magnetic current and force.