What is the Biot-Savart Law and How is it Used to Calculate Magnetic Fields?

[connor02]

Homework Statement

I have attached a diagram with the question.

Homework Equations

Biot-Savart law: (μ/4π)(I/r^2)(dlxr) or (μ/4π)(q/r^2)(dvxr)

The Attempt at a Solution

My question is,

The B field can be predicted from the right hand corkscrew rule right? So the part of the rod that exerts a B field on point P is only the small portion of the rod at the origin right?

The answer key shows some intergral over the whole length of the rod which I do not understand as I think the part of the rod that creates a B field at point P is only the little bit at the origin.

Thanks.

 

[Steely Dan]

The right hand rule is useful for determining the direction of the magnetic field, but do not let it fool you into thinking that it can give you any hints about the magnitude of said field. Even the parts of the current far away from the point contribute to the magnetic field at that point - they just contribute less and less, the farther away you get.

 

[connor02]

Ah i see. Aite, thank you.