Magnetic field at single point and straight line.

[cdummie]

Homework Statement

If i have a system with one linear conductor and point, it's not problem to determine magnetic field at point, nut what happens if i have to determine the magnetic field at the straight line parallel to the linear conductor.

Homework Equations

The Attempt at a Solution

For the linear conductor and point it's always B=(μ₀I)(sinθ₂-sinθ₁)/4πd. But i don't know how to do it if i have a straight line and linear conductor.

 

[mfb]

"The magnetic field" is always something you can determine at a single point - and the line just consists of many points. Determine the magnetic field for every point on the line and you are done.

 

[cdummie]

"The magnetic field" is always something you can determine at a single point - and the line just consists of many points. Determine the magnetic field for every point on the line and you are done.

So, it should go like this, when finding the magnetic field at the single point i integrate whole linear conductor i mean if it's very long, then i integrate from -π/2 to π/2 and when i do it, it's actually the magnetic field at the single point, and it looks like this B=(μ0I)/2πd, but what should i do next, how can i include whole line, not just this single point, should i integrate again or something?

 

[mfb]

What do you mean with "include whole line"? It's like asking "what is the temperature in the US?" - the answer will be "x here, y there, z over there, ...". It does not make sense to integrate over temperatures at various places.

Every point on the line has its own magnetic field strength, there is nothing to integrate over. If your conductor is an infinite line and your other line is parallel to it then the magnetic field strength will have the same value everywhere.

 

[cdummie]

What do you mean with "include whole line"? It's like asking "what is the temperature in the US?" - the answer will be "x here, y there, z over there, ...". It does not make sense to integrate over temperatures at various places.

Every point on the line has its own magnetic field strength, there is nothing to integrate over. If your conductor is an infinite line and your other line is parallel to it then the magnetic field strength will have the same value everywhere.

Thanks a lot, that's what i was looking for, so basically i need to find magnetic field at one point and i found it in every place in case of a infinite line, but what would happen if i had different conductor, say, conductor shaped like circle, would it be the same, i mean i find the magnetic field for one point and that's the value for the whole line, and if it's so, then why? Sorry for bothering (i just want to make it clear) and thanks again.

 

[mfb]

In general, different points will have different magnetic fields.