Magnetic Field Line Integral Problem

cjhseeker

1. The problem statement, all variables and given/known data

What is the line integral of B between points i and f in the figure?



2. Relevant equations

Ampere's Law: ∫B∙dl = Ienclosed * μ0
note: the integral on the left is a line integral.

3. The attempt at a solution

I applied Ampere's Law. I know that the contribution of B to the line integral on the straight segments to the left and right of the semicircle is zero since the magnetic field is perpendicular to the surface (line) at these segments. The semicircle, however, has a dl component that is parallel to the B field at all points along the semicircle. Therefore the integral should be B*pi*r (where r = 0.01 meters) and the right side of the equation should be 2A * μ0. I am confused as to whether the problem is asking for the value of the magnetic field, or whether I am supposed to simply give the value of ∫B∙dl.

pam

They want the integral.

cjhseeker

In that case, the integral is equal to the current enclosed by the surface, multiplied by the constant (mu). Is the value of the current enclosed 2A or 1A? This is a bit unclear to me due to the nature of the Amperian surface. Thank you for helping.

pam

The Amperian loop must be closed. Take it as a full circle for Ampere's law. Then, because of the symmetry, the integral on the half circle in the picture is half the full integral.