Question

A straight wire carrying a current of `12A` is bent into a semicircular arc of radius `2*0cm` as shown in figure. Consider the magnetic field `vecB` at the centre of arc.
(a) What is the magnetic field due to the staight segments?
(b) In what way the contribution to `vecB` from the semicircle differs from that of a circular loop and in what way does it resemble?
(c) Would your answer be different if the wire were bent into a semicircle arc of the same radius but in the opposite way as shown in figure

Answer 1

a) dl and r for each element of the straight segments are parallel. Therefore, `dl xx r =0` Straight segments do not contribute to |B|.
b) For all segments of the semicircular are `dlxxr` are all parallel to each other (into the plane of the paper). All such contributions add up in magnitude. Hence direction of B for a semicircular are is given by the right-hand ruele and magnitude is half that of a circular loop. Thus B is `1.9xx10^(-4) T` normal to the plane of the paper going into it. (c) Same magnitude of B but opposite in direction to that in (b).