Find Total Magnetic Flux Through a Wire and Loop

[azone]

a) There is an infinitely long wire carrying a current I. There is a square loop with resistance R a distance a from the wire in the same plane. Find the total magnetic flux through the loop.

b) There is an infinitely long wire carrying a current I in the z-direction. There is a square loop with resistance R a distance a from the wire in the xy plane. Find the total magnetic flux through the loop.

a) I know that the magnetic field from a straight wire is B=muo*I/2*pi*a. But isn't this just for a point a distance a away? What if it's a short line like the side of the loop? Does that mean I have to integrate? And also I know that there is no force on the two sides of the loop that is perpendicular to the wire, so does that mean that there is no magnetic field and hence no flux? So right now I guess I have a total magnetic field of B=mu*I/2*pi*a + mu*I/4*pi*a. And then I can find the flux from there.

b) I'm not sure at all how this wire affects the loop since they're not in the same plane. Does that mean there is no force on the loop at all? Or do I have to do some integration?

 

[siddharth]

a) I know that the magnetic field from a straight wire is B=muo*I/2*pi*a. But isn't this just for a point a distance a away? What if it's a short line like the side of the loop? Does that mean I have to integrate?

Notice that the question is asking for the magnetic flux through the loop. You'll need to evaluate $$\int \vec{B} \cdot d \vec{A}$$ over the area enclosed by the loop.

And also I know that there is no force on the two sides of the loop that is perpendicular to the wire, so does that mean that there is no magnetic field and hence no flux?

No. How did you come to this conclusion?

b) I'm not sure at all how this wire affects the loop since they're not in the same plane. Does that mean there is no force on the loop at all? Or do I have to do some integration?

Do the same integration. What direction is the magnetic field due to the wire? What direction is the area vector? So, what can you say about $$\vec{B} \cdot d\vec{A}$$?