Comments related to h2-003 and 004

In last lecture you saw how to determine B at the center of a circular arc with angle theta and the line segment at any point. For a review, see discussions of Lec17-3 and Lec18-1 in the “clicker questions”. At this point you are armed with the tools which should enable you to solve essentially all the Biot-Savart problems in this course.

Let me use ch8-h2 003-004 as an example to illustrate the application. Here the current configuration consists of 3 pieces, the vertical line segment, the circular arc which has an angle 90 deg and a horizontal line segment.

First you need to determine the direction of B contributed by each of the segments and verify the direction of DB at any point along the path should be  pointing outward. This implies that the original vector equation can now be reduced to an algebraic equation, i.e.  

from  B=B nhat=B1 nhat +B2 nhat +B3 nhat, to B=B1+B2+B3.  

In the second equation says that the resultant magnitude of B equals to the sum of the individual contributions.  

For each line segment contribution, you should study the explanation on the semi-long wire in the slides of Lec18-1. Pay attention to the factor:  (cos alpha1- cos alpha2) see how it is defined and how it is evaluated.    For question 004, For each line segment in 004, you should identify the corresponding alpha1 and alpha2 and  convince youself, for each case should turn out to be 1.

Thank you for your attention,

C. Chiu